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֐̔ II i֐̏̓֐j

$3\displaystyle{{ \{ \frac{\hspace{2} h \(x\) \hspace{2}}{\hspace{2} g \(x\) \hspace{2}} \} }^{\prime }=\frac{\hspace{2} {h}^{\prime } \(x\) g \(x\) - h \(x\) {g}^{\prime } \(x\) \hspace{2}}{\hspace{2} { \{ g \(x\) \} }^{2} \hspace{2}}}$

Ȃ킿C

$3\displaystyle{ f \(x\) =\frac{\hspace{2} h \(x\) \hspace{2}}{\hspace{2} g \(x\) \hspace{2}} }$ $3\displaystyle{ \rightarrow {f}^{\prime } \(x\) =\frac{\hspace{2} {h}^{\prime } \(x\) g \(x\) - h \(x\) {g}^{\prime } \(x\) \hspace{2}}{\hspace{2} { \{ g \(x\) \} }^{2} \hspace{2}} }$

o

$3\displaystyle{ {f}^{\prime } \(x\) ={\lim}\limits_{ h\rightarrow 0 }\frac{\hspace{2} f \( x+ h \) - f \(x\) \hspace{2}}{\hspace{2}h\hspace{2}} }$

$3\displaystyle{ ={\lim}\limits_{ h\rightarrow 0 }\frac{\hspace{2} \frac{\hspace{2} h \( x+ h \) \hspace{2}}{\hspace{2} g \( x+ h \) \hspace{2}}- \frac{\hspace{2} h \(x\) \hspace{2}}{\hspace{2} g \(x\) \hspace{2}} \hspace{2}}{\hspace{2}h\hspace{2}} }$

$3\displaystyle{ ={\lim}\limits_{ h\rightarrow 0 }\frac{\hspace{2}\frac{\hspace{2} h \( x+ h \) g \(x\) - h \(x\) g \( x+ h \) \hspace{2}}{\hspace{2} g \( x+ h \) g \(x\) \hspace{2}}\hspace{2}}{\hspace{2}h\hspace{2}} }$

• $3\displaystyle{\displaystyle{={\lim}\limits_{ h\rightarrow 0 } \{ \frac{\hspace{2}1\hspace{2}}{\hspace{2} g \( x+ h \) g \(x\) \hspace{2}}\cdot }}$

• $3\displaystyle{\displaystyle{ \frac{\hspace{2} h \( x+ h \) g \(x\) - h \(x\) g \( x+ h \) \hspace{2}}{\hspace{2}h\hspace{2}} \} }}$

• $3\displaystyle{ = \{ {\lim}\limits_{ h\rightarrow 0 }\frac{\hspace{2}1\hspace{2}}{\hspace{2} g \( x+ h \) g \(x\) \hspace{2}} \} }$

• $3\displaystyle{ \{ {\lim}\limits_{ h\rightarrow 0 }\frac{\hspace{2} h \( x+ h \) g \(x\) - h \(x\) g \(x\) + h \(x\) g \(x\) - h \(x\) g \( x+ h \) \hspace{2}}{\hspace{2}h\hspace{2}} \} }$

• $3\displaystyle{ = \{ {\lim}\limits_{ h\rightarrow 0 }\frac{\hspace{2}1\hspace{2}}{\hspace{2} g \( x+ h \) g \(x\) \hspace{2}} \} }$

• $3\displaystyle{ \{ {\lim}\limits_{ h\rightarrow 0 }\frac{\hspace{2} \{ h \( x+ h \) - h \(x\) \} g \(x\) + h \(x\) \{ g \(x\) - g \( x+ h \) \} \hspace{2}}{\hspace{2}h\hspace{2}} \} }$

• $3\displaystyle{ = \{ {\lim}\limits_{ h\rightarrow 0 }\frac{\hspace{2}1\hspace{2}}{\hspace{2} g \( x+ h \) g \(x\) \hspace{2}} \} }$

• $3\displaystyle{ \[ \{ {\lim}\limits_{ h\rightarrow 0 }\frac{\hspace{2} h \( x+ h \) - h \(x\) \hspace{2}}{\hspace{2}h\hspace{2}} \} g \(x\) - h \(x\) \{ {\lim}\limits_{ h\rightarrow 0 }\frac{\hspace{2} g \( x+ h \) - g \(x\) \hspace{2}}{\hspace{2}h\hspace{2}} \} \] }$

$3\displaystyle{ =\frac{\hspace{2} {h}^{\prime } \(x\) g \(x\) - h \(x\) {g}^{\prime } \(x\) \hspace{2}}{\hspace{2} { \{ g \(x\) \} }^{2} \hspace{2}} }$

Q

āC

$3\displaystyle{{ \{ \frac{\hspace{2} h \(x\) \hspace{2}}{\hspace{2} g \(x\) \hspace{2}} \} }^{\prime }=\frac{\hspace{2} {h}^{\prime } \(x\) g \(x\) - h \(x\) {g}^{\prime } \(x\) \hspace{2}}{\hspace{2} { \{ g \(x\) \} }^{2} \hspace{2}}}$

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