Question

differentiation of Cos root x

Answer 1

This method is called chain rule.
you just need to remember the differentiation of cosx.

Answer 2

Hey There!



Here, we can differentiate as follows:


$Ans =\frac{d}{dx}\cos\sqrt{x} \\ \\ \\ \\ Let \,\, u=\sqrt{x} \\ \\ \implies \frac{du}{dx} = \frac{1}{2}x^{\frac{1}{2}-1} = \frac{1}{2\sqrt{x}} \\ \\ \\ \\ \implies Ans = \frac{d}{dx} \cos u \\ \\ \\ \implies Ans = -\sin u \, \frac{du}{dx} \\ \\ \\ \boxed{Ans = -\frac{\sin \sqrt{x}}{2\sqrt{x}}}$



Hope it helps
Purva
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