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Question

For some constant a and b, find the derivative of the following functions:
(ax2+b)2.

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Solution

Let f(x)=(ax2+b)2
f(x)=a2x4+2abx2+b2
f(x)=ddx(a2x4+2abx2)=a2ddx(x4)+2abddx(x2)+ddx(b2)
=a2(4x3)+2ab(2x)+b2(0)
=4a2x3+4abx=4ax(ax2+b)

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