Q. The derivative of $F\lbrack f\left\{ \phi(x) \right\}\rbrack$is
A) $F'\left\lbrack f\left\{ \phi(x) \right\} \right\rbrack$
B) $F^{'}\left\lbrack f\left\{ \phi(x) \right\} \right\rbrack f\{\phi(x)\}$
C) $F^{'}\left\lbrack f\left\{ \phi(x) \right\} \right\rbrack f'\{\phi(x)\}$
D) $F^{'}\left\lbrack f\left\{ \phi(x) \right\} \right\rbrack f^{'}\left\{ \phi(x) \right\}\phi^{'}(x)$
Explanation
(d)
Let $y = F\{ f\left( \phi(x) \right)\}$
On differentiating w.r.t. $x$, we get
$y^{'} = F^{'}\left\lbrack f\left\{ \phi(x) \right\} \right\rbrack\frac{d}{dx}f\{\phi(x)\}$
${= F^{'}\left\lbrack f\left\{ \phi(x) \right\} \right\rbrack f^{'}\left\{ \phi(x) \right\}\frac{d}{dx}\phi(x)
}{= F^{'}\left\lbrack f\left\{ \phi(x) \right\} \right\rbrack f^{'}\left\{ \phi(x) \right\}\phi^{'}(x)}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.