uEU[̖߂{^ʂɖ߂Ȃꍇ ͂{^ĂB
 ݂̐̃TCY 3 łB TCYI 2 3 4 5 6 7
 Tweet ̃y[W
@

# Δ̖艉K

1. ̊֐ΔD
 $3\displaystyle{z=x- 2y}$ $3\displaystyle{z={x}^{2}+{y}^{2}}$ $3\displaystyle{z={x}^{2}- 3xy+2{y}^{2}}$ $3\displaystyle{z=\frac{\hspace{2}y\hspace{2}}{\hspace{2}x\hspace{2}}}$ @ $3\displaystyle{z=\frac{\hspace{2} x- y \hspace{2}}{\hspace{2} x+y \hspace{2}}}$ $3\displaystyle{z=\sqrt{ 3x- 4y }}$ $3\displaystyle{z={e}^{ xy }}$ $3\displaystyle{z=\log \( x- y \) }$ $3\displaystyle{z=2\sin \sqrt{ xy }}$ $3\displaystyle{z={\tan }^{ - 1 }\frac{\hspace{2}y\hspace{2}}{\hspace{2}x\hspace{2}}}$ $3\displaystyle{z={x}^{3}+3{x}^{2}y+2{y}^{3}}$ $3\displaystyle{z={e}^{ - ax }\text{\hspace{1}\hspace{1}} \( \sin by+\cos by \) }$ $3\displaystyle{f \( x,y \) =\frac{\hspace{2} 5x+3y \hspace{2}}{\hspace{2} 3x+2y \hspace{2}}}$ $3\displaystyle{f \( x,y \) ={x}^{y}}$
2. ̊֐ɂ $3\displaystyle{\text{\hspace{1}}\text{\hspace{1}}\frac{\hspace{2}{\partial}\hspace{2}}{\hspace{2} {\partial}x \hspace{2}}f \( 1,- 2 \) \text{\hspace{1}}\text{\hspace{1}}}$ $3\displaystyle{\text{\hspace{1}}\text{\hspace{1}}\frac{\hspace{2}{\partial}\hspace{2}}{\hspace{2} {\partial}y \hspace{2}}f \( - 1,2 \) \text{\hspace{1}}\text{\hspace{1}}}$ ߂D
 $3\displaystyle{f \( x,y \) ={x}^{2}+xy- {y}^{2}}$ $3\displaystyle{f \( x,y \) =\sqrt{ {x}^{2}- xy }}$ $3\displaystyle{ f \( x,y \) ={ \sin }^{ - 1 }\frac{\hspace{2}x\hspace{2}}{\hspace{2}y\hspace{2}} }$
3. ̂ƂؖD
 $3\displaystyle{z=f \( \frac{\hspace{2}y\hspace{2}}{\hspace{2}x\hspace{2}} \) \text{\hspace{1}}\text{\hspace{1}}}$ Ȃ $3\displaystyle{\text{\hspace{1}}\text{\hspace{1}}x\frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}x \hspace{2}}+y\frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}y \hspace{2}}=0\text{\hspace{1}}\text{\hspace{1}}}$ łD $3\displaystyle{z=f \( {x}^{2}- {y}^{2} \) \text{\hspace{1}\hspace{1}}}$ Ȃ $3\displaystyle{\text{\hspace{1} }\text{\hspace{1} }y\frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}x \hspace{2}}+x\frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}y \hspace{2}}=0\text{\hspace{1} }\text{\hspace{1} }}$ łD $3\displaystyle{z=\frac{\hspace{2}1\hspace{2}}{\hspace{2}x\hspace{2}}f \( \frac{\hspace{2}y\hspace{2}}{\hspace{2}x\hspace{2}} \) \text{\hspace{1} }\text{\hspace{1} }}$ Ȃ $3\displaystyle{\text{\hspace{1} }\text{\hspace{1} }x\frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}x \hspace{2}}+y\frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}y \hspace{2}}+z=0\text{\hspace{1} }\text{\hspace{1} }}$ łD $3\displaystyle{z=\log \sqrt{ {x}^{2}+{y}^{2} }\text{\hspace{1} }\text{\hspace{1} }}$ Ȃ $3\displaystyle{\text{\hspace{1} }\text{\hspace{1} }{ \( \frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}x \hspace{2}} \) }^{2}+{ \( \frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}y \hspace{2}} \) }^{2}=\frac{\hspace{2}1\hspace{2}}{\hspace{2} {e}^{ 2z } \hspace{2}}\text{\hspace{1} }\text{\hspace{1} }}$ łD
4. ̊֐ $3\displaystyle{\frac{\hspace{2} dz \hspace{2}}{\hspace{2} dt \hspace{2}}}$ ߂D
 $3\displaystyle{z=f \( x,y \) \text{\hspace{1} },}$ $3\displaystyle{\text{\hspace{1} \hspace{1} \hspace{1} \hspace{1} \hspace{1} \hspace{1} }x=a+ht\text{\hspace{1} },\text{\hspace{1} }\text{\hspace{1} }y=b+kt\text{\hspace{1} }\text{\hspace{1} }}$ $3\displaystyle{z={x}^{2}+{y}^{2}\text{\hspace{1} },}$ $3\displaystyle{\text{\hspace{1} \hspace{1} \hspace{1} \hspace{1} \hspace{1} \hspace{1} }x=t- \sin t\text{\hspace{1} },\text{\hspace{1} }\text{\hspace{1} }y=1- \cos t\text{\hspace{1} }\text{\hspace{1} }}$ $3\displaystyle{z=xy\text{\hspace{1} },}$ $3\displaystyle{\text{\hspace{1} \hspace{1} \hspace{1} \hspace{1} \hspace{1} \hspace{1} }x=2{t}^{2}+1\text{\hspace{1} },\text{\hspace{1} }\text{\hspace{1} }y={t}^{2}+3t+1\text{\hspace{1} }\text{\hspace{1} }}$ $3\displaystyle{z=x\tan y\text{\hspace{1} },}$ $3\displaystyle{\text{\hspace{1} \hspace{1} \hspace{1} \hspace{1} \hspace{1} \hspace{1} }x={\sin }^{ - 1 }2t\text{\hspace{1} },\text{\hspace{1} }\text{\hspace{1} }y={\cos }^{ - 1 }2t\text{\hspace{1} }\text{\hspace{1} }}$
5. ̂ƂD
 $3\displaystyle{z=f \( x,y \) }$ , $3\displaystyle{x=r\cos {\theta}}$ , $3\displaystyle{y=r\sin {\theta}}$ Ȃ $3\displaystyle{{ \( \frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}x \hspace{2}} \) }^{2}+{ \( \frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}y \hspace{2}} \) }^{2}={ \( \frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}r \hspace{2}} \) }^{2}+\frac{\hspace{2}1\hspace{2}}{\hspace{2} {r}^{2} \hspace{2}}{ \( \frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}{\theta} \hspace{2}} \) }^{2}}$ ƂȂD $3\displaystyle{z=f \( x,y \) \text{\hspace{1} },\text{\hspace{1} }\text{\hspace{1} }x=u\cos {\alpha}- v\sin {\alpha}\text{\hspace{1} },\text{\hspace{1} }\text{\hspace{1} }y=u\sin {\alpha}+v\cos {\alpha}\text{\hspace{1} }\text{\hspace{1} }}$ Ȃ $3\displaystyle{{ \( \frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}x \hspace{2}} \) }^{2}+{ \( \frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}y \hspace{2}} \) }^{2}={ \( \frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}u \hspace{2}} \) }^{2}+{ \( \frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}v \hspace{2}} \) }^{2}\text{\hspace{1} }\text{\hspace{1} }}$ ƂȂD
6. ̊֐̑2Γ֐߂D
 $3\displaystyle{z=3x- 2y}$ $3\displaystyle{z={x}^{3}+{y}^{3}}$ $3\displaystyle{z=2{x}^{2}- 3xy+4{y}^{2}}$ $3\displaystyle{z=\frac{\hspace{2}y\hspace{2}}{\hspace{2}x\hspace{2}}}$ $3\displaystyle{z=\frac{\hspace{2} x- y \hspace{2}}{\hspace{2} x+y \hspace{2}}}$ $3\displaystyle{z=\sqrt{ 2x- 3y }}$ $3\displaystyle{z={e}^{ xy }}$ $3\displaystyle{z=\log \( x- y \) }$ $3\displaystyle{z=\sin \sqrt{ xy }}$ $3\displaystyle{z={\tan }^{ - 1 }\text{\hspace{1} }\frac{\hspace{2}y\hspace{2}}{\hspace{2}x\hspace{2}}}$
7. ̊֐̑2Γ֐߂D
 $3\displaystyle{z=f \( x,y \) \text{\hspace{1} },}$ $3\displaystyle{\text{\hspace{1} \hspace{1} \hspace{1} \hspace{1} \hspace{1} \hspace{1} }x=t- \sin t\text{\hspace{1} },\text{\hspace{1} }\text{\hspace{1} }y=1- \cos t\text{\hspace{1} }\text{\hspace{1} }}$ $3\displaystyle{z=f \( x,y \) \text{\hspace{1} },}$ $3\displaystyle{\text{\hspace{1} \hspace{1} \hspace{1} \hspace{1} \hspace{1} \hspace{1} }x=2{t}^{2}- 3\text{\hspace{1} },\text{\hspace{1} }\text{\hspace{1} }y={t}^{2}+3t+7\text{\hspace{1} }\text{\hspace{1} }}$
8. ̂ƂD
 $3\displaystyle{z=f \( x,y \) \text{\hspace{1} },\text{\hspace{1} }\text{\hspace{1} }x=u\cos {\theta}- v\sin {\theta}\text{\hspace{1} },\text{\hspace{1} }\text{\hspace{1} }y=u\sin {\theta}+v\cos {\theta}\text{\hspace{1} }\text{\hspace{1} }}$ ̂Ƃ $3\displaystyle{\frac{\hspace{2} {{\partial}}^{2}z \hspace{2}}{\hspace{2} {\partial}{x}^{2} \hspace{2}}+\frac{\hspace{2} {{\partial}}^{2}z \hspace{2}}{\hspace{2} {\partial}{y}^{2} \hspace{2}}=\frac{\hspace{2} {{\partial}}^{2}z \hspace{2}}{\hspace{2} {\partial}{u}^{2} \hspace{2}}+\frac{\hspace{2} {{\partial}}^{2}z \hspace{2}}{\hspace{2} {\partial}{v}^{2} \hspace{2}}\text{\hspace{1} }\text{\hspace{1} }}$ ƂȂD $3\displaystyle{z=f \( x,y \) \text{\hspace{1}},\text{\hspace{1}}\text{\hspace{1}}x=r\cos {\theta}\text{\hspace{1}},\text{\hspace{1}}\text{\hspace{1}}y=r\sin {\theta}\text{\hspace{1}}\text{\hspace{1}}}$ ̂Ƃ $3\displaystyle{\frac{\hspace{2} {{\partial}}^{2}z \hspace{2}}{\hspace{2} {\partial}{x}^{2} \hspace{2}}+\frac{\hspace{2} {{\partial}}^{2}z \hspace{2}}{\hspace{2} {\partial}{y}^{2} \hspace{2}}=\frac{\hspace{2} {{\partial}}^{2}z \hspace{2}}{\hspace{2} {\partial}{r}^{2} \hspace{2}}+\frac{\hspace{2}1\hspace{2}}{\hspace{2}r\hspace{2}}\frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}r \hspace{2}}+\frac{\hspace{2}1\hspace{2}}{\hspace{2} {r}^{2} \hspace{2}}\frac{\hspace{2} {{\partial}}^{2}z \hspace{2}}{\hspace{2} {\partial}{{\theta}}^{2} \hspace{2}}\text{\hspace{1}}\text{\hspace{1}}}$ ƂȂD
9. ̂ƂD
 $3\displaystyle{y=f \( x,t \) }$ ɂāC1̔g $3\displaystyle{\frac{\hspace{2} {{\partial}}^{2}y \hspace{2}}{\hspace{2} {\partial}{t}^{2} \hspace{2}}={c}^{2}\frac{\hspace{2} {{\partial}}^{2}y \hspace{2}}{\hspace{2} {\partial}{x}^{2} \hspace{2}}}$ $3\displaystyle{\text{\hspace{1} }\text{\hspace{1} }{\xi}=x- ct\text{\hspace{1} },\text{\hspace{1} }\text{\hspace{1} }{\eta}=x+ct\text{\hspace{1} }\text{\hspace{1} }}$ Ȃϊs $3\displaystyle{\frac{\hspace{2} {{\partial}}^{2}y \hspace{2}}{\hspace{2} {\partial}{\eta}{\partial}{\xi} \hspace{2}}=0}$ ƂȂD $3\displaystyle{z}$ Ɋւ $3\displaystyle{\frac{\hspace{2} {{\partial}}^{2}z \hspace{2}}{\hspace{2} {\partial}{t}^{2} \hspace{2}}={c}^{2} \( \frac{\hspace{2} {{\partial}}^{2}z \hspace{2}}{\hspace{2} {\partial}{r}^{2} \hspace{2}}+\frac{\hspace{2}2\hspace{2}}{\hspace{2}r\hspace{2}}\frac{\hspace{2} {\partial}z \hspace{2}}{\hspace{2} {\partial}r \hspace{2}} \) }$ ɂāC $3\displaystyle{z=\frac{\hspace{2}1\hspace{2}}{\hspace{2}r\hspace{2}}u}$ ƂC $3\displaystyle{u}$ Ɋւɕϊ $3\displaystyle{\frac{\hspace{2} {{\partial}}^{2}u \hspace{2}}{\hspace{2} {\partial}{t}^{2} \hspace{2}}={c}^{2}\frac{\hspace{2} {{\partial}}^{2}u \hspace{2}}{\hspace{2} {\partial}{r}^{2} \hspace{2}}}$ ƂȂ
10. ̊֌WŒ` $3\displaystyle{\text{\hspace{1} }\text{\hspace{1} }y={\varphi} \(x\) \text{\hspace{1} }\text{\hspace{1} }}$ ɂ $3\displaystyle{\text{\hspace{1} }\text{\hspace{1} }\frac{\hspace{2} {d}^{2}y \hspace{2}}{\hspace{2} d{x}^{2} \hspace{2}}\text{\hspace{1} }\text{\hspace{1} }}$ ߂D
 $3\displaystyle{3{x}^{2}+2xy+{y}^{2}=1}$ $3\displaystyle{{y}^{2}=4px}$ $3\displaystyle{\frac{\hspace{2} {x}^{2} \hspace{2}}{\hspace{2} {a}^{2} \hspace{2}}+\frac{\hspace{2} {y}^{2} \hspace{2}}{\hspace{2} {b}^{2} \hspace{2}}=1}$ $3\displaystyle{y={e}^{ x+y }}$ $3\displaystyle{\log \text{\hspace{1} }\sqrt{ {x}^{2}+{y}^{2} }- {\tan }^{ - 1 }\text{\hspace{1} }\frac{\hspace{2}y\hspace{2}}{\hspace{2}x\hspace{2}}=0}$ $3\displaystyle{{x}^{3}+{y}^{3}- 3axy=0}$
11. ̊֌WŒ` $3\displaystyle{\text{\hspace{1} }\text{\hspace{1} }y={\varphi} \(x\) \text{\hspace{1} }\text{\hspace{1} }}$ ̎w肳ꂽ_ɂڐ̕߂D
 $3\displaystyle{\text{\hspace{1} \hspace{1} }f \( x,y \) =0\text{\hspace{1} }\text{\hspace{1} }}$ ̓_ $3\displaystyle{\text{\hspace{1} } \( a,b \) \text{\hspace{1} }\text{\hspace{1} }}$ ł̐ڐ̕ $3\displaystyle{\text{\hspace{1} \hspace{1} }{x}^{3}+{y}^{3}- xy=0\text{\hspace{1} \hspace{1} }}$ ̓_ $3\displaystyle{\text{\hspace{1} } \( \frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}},\frac{\hspace{2}1\hspace{2}}{\hspace{2}2\hspace{2}} \) \text{\hspace{1} }\text{\hspace{1} }}$ ɂڐ̕
12. ̊֌WŒ` $3\displaystyle{\text{\hspace{1} }\text{\hspace{1} }y={\varphi} \(x\) \text{\hspace{1} }\text{\hspace{1} }}$ ̋ɒl𒲂ׂD
 $3\displaystyle{{x}^{2}- 2xy+3{y}^{2}=8}$ $3\displaystyle{{x}^{2}y- x{y}^{2}+128=0}$ $3\displaystyle{{x}^{2}{y}^{2}- 2x+9{y}^{2}=0}$ $3\displaystyle{{x}^{3}- 12xy+2{y}^{3}=0}$ $3\displaystyle{{x}^{4}- 16xy+3{y}^{4}=0}$ $3\displaystyle{{x}^{4}+4{x}^{2}+3{y}^{3}- 2y=0}$ $3\displaystyle{{x}^{2}+2xy+{y}^{4}+2{y}^{2}=6}$
13. ̂ƂD
 $3\displaystyle{z=xf \( ax+by \) +yg \( ax+by \) \text{\hspace{1} }}$Ȃ $3\displaystyle{{b}^{2}\frac{\hspace{2} {{\partial}}^{2}z \hspace{2}}{\hspace{2} {\partial}{x}^{2} \hspace{2}}- 2ab\frac{\hspace{2} {{\partial}}^{2}z \hspace{2}}{\hspace{2} {\partial}x{\partial}y \hspace{2}}+{a}^{2}\frac{\hspace{2} {{\partial}}^{2}z \hspace{2}}{\hspace{2} {\partial}{y}^{2} \hspace{2}}=0}$ ł
14. ̊֐̋ɒl߂D
 $3\displaystyle{f \( x,y \) ={x}^{2}+2{y}^{2}+10x}$ $3\displaystyle{f \( x,y \) ={x}^{2}- 2xy+3{y}^{2}- 4x+5y}$ $3\displaystyle{f \( x,y \) =4{x}^{2}+2xy+{y}^{2}+4x+4y}$ $3\displaystyle{f \( x,y \) =xy \( x- 2y- 3 \) }$ $3\displaystyle{f \( x,y \) ={x}^{3}+{y}^{3}- 12x- 27y}$ $3\displaystyle{f \( x,y \) ={x}^{3}+{y}^{3}+6xy- 24}$ $3\displaystyle{f \( x,y \) =xy+\frac{\hspace{2}1\hspace{2}}{\hspace{2}x\hspace{2}}+\frac{\hspace{2}1\hspace{2}}{\hspace{2}y\hspace{2}}}$ $3\displaystyle{f \( x,y \) =\cos x+\cos y+\cos \( x+y \) }$ $3\displaystyle{\text{\hspace{1} }\text{\hspace{1} }\text{\hspace{1} }\text{\hspace{1} }\text{\hspace{1} }\text{\hspace{1} } \( 0< x\text{\hspace{1} },\text{\hspace{1} }y< {\pi} \) }$

z[>>JeS[>>>>Δ>>艉K

wX^bt쐬

ŏIXVF 2013N822

 [y[Wgbv]