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20 March, 07:47

Find f ′ (x) for f (x) = sin (3x2).

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  1. 20 March, 10:54
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    Assuming you mean f (x) = sin (3x²)

    Use chain rule to differentiate as we can view this as a composite function.

    The outside "function" is sin (x); the inside "function" is 3x^2

    The derivative of the composite function we get by

    ⇒ Differentiating the outside function: so we have cos (x). Then stick the inside function into that.

    ⇒ After that, multiply by the derivative of the inside function. The derivative of the inside function is 6x.

    f (x) = sin (3x²)

    f' (x) = cos (3x²) · (3x²) '

    f' (x) = cos (3x²) · 6x

    f' (x) = 6x cos (3x²)

    The answer is f' (x) = 6x cos (3x²)
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