How do you find the derivative of $y=6 cos(x^3+3)$ ?

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How do you find the derivative of $y=6 cos(x^3+3)$ ?

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Answer 1 · 2014-07-24T22:34:34

This is a composite of the function $x^3+3$ and the function $6cos x$ , so we will need the Chain Rule together with $(x^3+3)=3x^2$ and $(cos x)'=-sin x$ (as shown here:derivative of trig functions ).

Thus
$(6cos(x^3+3))'=-6sin(x^3+3)\times (x^3+3)'=-18x^2 sin(x^3+3)$ .

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How do you find the derivative of $y=6 cos(x^3+3)$ ?

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