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  • Differentiate the functions with respect to x in cos sin x

2. Differentiate the functions with respect to x in 

\cos ( \sin x )

Answers (1)

best_answer

Given function is
f(x)= \cos ( \sin x )
Lets take t = \sin x  then,
f(t) = \cos t
\frac{df(t)}{dx} = \frac{df(t)}{dt}.\frac{dt}{dx}                            ( By chain rule)
\frac{df(t)}{dt} = \frac{d(\cos t)}{dt} = -\sin t = -\sin (\sin x)
\frac{dt}{dx} = \frac{d(\sin x)}{dt} = \cos x
Now,
\frac{df(t)}{dx} = \frac{df(t)}{dt}.\frac{dt}{dx} = -\sin(\sin x).\cos x
Therefore, the answer is -\sin(\sin x).\cos x
 

Posted by

Gautam harsolia

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