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    IBMediumCalculus10–12

    Derivative of Composite Function

    Derivada de Função Composta

    Find the derivative of f(x)=sin⁡(x2+1)f(x) = \sin(x^{2} + 1). Use the chain rule and express your answer in simplified form.

    Apply the chain rule: if f(x)=sin⁡(g(x))f(x) = \sin(g(x)), then f′(x)=cos⁡(g(x))⋅g′(x)f'(x) = \cos(g(x)) \cdot g'(x). Here g(x)=x2+1g(x) = x^{2} + 1.

    Solution

    Step 1 of 4

    1. 1.Using the chain rule: