8. Differentiate the functions with respect to x in 

\cos ( \sqrt x ) 

Answers (1)

Given function is
f(x) = \cos(\sqrt x )
Let's take \sqrt x = t
Then, our function becomes
f(t) = \cos t
Now, differentiation w.r.t. x
\frac{d(f(t))}{dx} = \frac{d(f(t))}{dt}.\frac{dt}{dx}                     -(By chain rule)
\frac{d(f(t))}{dt} = \frac{d(\cos t)}{dt} = -\sin t = -\sin (\sqrt x) \ \ \ \ \ \ (\because \sqrt x = t)
\frac{dt}{dx} = \frac{d(\sqrt x)}{dt} = \frac{1}{2\sqrt x}
Now,
\frac{d(f(t))}{dx} =-\sin(\sqrt x).\frac{1}{2\sqrt x}
Therefore, the answer is \frac{-\sin(\sqrt x)}{2\sqrt x}


 

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