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Thread: Differentiation

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    Differentiation

    Find the derivative of $\displaystyle tan^{-1}(x^2)$.

    Could someone explain how to solve this?
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    Quote Originally Posted by Haris View Post
    Find the derivative of $\displaystyle tan^{-1}(x^2)$.

    Could someone explain how to solve this?
    Chain rule. Let $\displaystyle u = x^2 $ so $\displaystyle y = \tan^{-1} u$. So

    $\displaystyle \frac{dy}{dx} = \frac{dy}{du}\, \cdot \, \frac{du}{dx}$ and calculating each derivative gives $\displaystyle \frac{dy}{du} = \frac{1}{1+u^2}$ and $\displaystyle \frac{du}{dx} = 2x$.

    Substituting gives

    $\displaystyle \frac{dy}{dx} = \frac{1}{1+u^2}\, \cdot2x = \frac{2x}{1+x^4}.$
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