Question

Differentiate the following with respect to x.

sin(x²)

Answer 1

For the following problems chain rule to be used:

`"d"/"dx"` f(g(x)) = f'(g(x)) . g'(x)

`"d"/"dx"` [f(x)]ⁿ = n[f(x)]^n-1 × `"d"/"dx"`f(x)

Let y = sin(x²) 

`"dy"/"dx"` f(g(x)) = f'(g(x)) . g'(x)

Here f = sin x, g = x²

`"dy"/"dx" = cos(x^2) "d"/"dx" (x^2)`

= cos(x²) (2x)

= 2x cos(x²)