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Math Help - Differentiation

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    Differentiation

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

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

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

    Substituting gives

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