How do you differentiate $f(x)= x^2*tan^-1 x$ ?

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How do you differentiate $f(x)= x^2*tan^-1 x$ ?

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Answer 1 · 2015-06-10T03:17:30

The answer is $f'(x)=x^2/(1+x^2)+2x tan^{-1}(x)$

Explanation:

This follows from the Product Rule $d/dx(g(x)h(x))=g(x)h'(x)+g'(x)h(x)$ (with $g(x)=x^2$ and $h(x)=tan^{-1}(x)$ ), the Power Rule $d/dx(x^(n))=nx^(n-1)$ , and the derivative of inverse tangent $d/dx(tan^{-1}(x))=1/(1+x^2)$ .

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How do you differentiate $f(x)= x^2*tan^-1 x$ ?

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