1. Differentiate the functions with respect to x in 

\sin (x^2 +5 )

Answers (1)

Given function is
f(x)=\sin (x^2 +5 )
when we differentiate it w.r.t. x.
Lets take t = x^2+5 . then,
f(t) = \sin t
\frac{df(t)}{dx} = \frac{df(t)}{dt}.\frac{dt}{dx}                                          (By  chain rule)
\frac{df(t)}{dt} = \frac{d(\sin t )}{dt} = \cos t = \cos (x^2+5)
\frac{dt}{dx} = \frac{d(x^2+5 )}{dx} = 2x
Now,
\frac{df(t)}{dx} = \frac{df(t)}{dt}.\frac{dt}{dx} = \cos (x^2+5).2x
Therefore, the answer is 2x \cos (x^2+5)

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