## Related questions with answers

Question

Evaluate the derivative of the following functions. $f(w)=w^{2}-\tan ^{-1} w^{2}$

Solution

VerifiedStep 1

1 of 3$f'(w)=(w^2-\tan^{-1}w^2)'=\\ \\ \\ (w^2)'-\underbrace{(\tan^{-1}w^2)'}_{\color{#4257b2}\text{(A)}}=\\ \\ \\ 2w-\dfrac{2w}{1+w^4}=\\ \\ \\ \dfrac{2w+2w^5}{1+w^4}-\dfrac{2w}{1+w^4}=\\ \\ \\ \dfrac{2w+2w^5-2w}{1+w^4}=\boxed{\dfrac{2w^5}{1+w^4}}$

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