Question

How do you differentiate `cos(x^2)/(e^(x^2)+1)`?

Answer 1

`f'(x)=(2x(-e^(x^2)(sin(x^2)+cos(x^2))-sin(x^2)))/(e^(x^2)+1)^2`

Explanation:

We will use the quotient rule

`(u/v)'=(u'v-uv')/v^2`

so we get

`f'(x)=(-sin(x^2)2x(e^(x^2)+1)-cos(x^2)*e^(x^2)*2x)/(e^(x^2)+1)^2`

simplifying we get

`f'(x)=(2x(-e^(x^2)(sin(x^2)+cos(x^2))-sin(x^2)))/(e^(x^2)+1)^2`