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

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Answer 1 · 2018-07-17T17:02:15

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

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#