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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