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How do you differentiate #f(x) = x/sqrt(sin^2(1+x^2) # using the chain rule?

1 Answer

Nov 1, 2016

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

Explanation:

#f(x)=x/(sqrt(sin^2(1+x^2))#

Use quotient rule and chain rule

#f=x, g=((sin(1+x^2))^2)^(1/2) = sin(1+x^2)#

#f'=1, g'=cos(1+x^2)*2x#

#f'(x)=(gf'-fg')/g^2#

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

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