Question

differentiation of sin x square​

Answer 1

Explanation:

$Let \: y \: = {sin}x^{2} \\ \frac{dy}{dx} = \frac{d}{dx} {sin}x^{2} \\ = \: \cos \: x^2 \: \frac{d}{dx} \: x^2 \\ = \: \cos \: x^2\: 2 \: x \: \\ =2x\:cos \: x^2$

Answer 2

Answer:

f(x) = (sin x)2 can be written as f(u) = u2 where u = sin x. The Chain Rule states that to differentiate a composite function we differentiate the outer function and multiply by the derivative of the inner function. We can use the rules cos x = sin ( /2– x) and sin x = cos( /2 – x) to find the derivative of cos x.