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Question
For some constants a and b, find the derivative of (ax2 + b)2.
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Solution
Let f(x) = (ax2 + b2)
= f(x) = a2x4 + 2abx2 + b2
∴ `f'(x) = d/(dx) (a^2 x^4 + 2abx^2 + b^2) = a^2 d/(dx) (x^4) + 2ab d/(dx) (x^2) + d/(dx)(b^2)`
Using the theorem `d/(dx) x^n = nx^(n - 1)`, we obtain
∴ f'(x) = a2 (4x3) + 2ab (2x) + b20
= 4a2x3 + 4abx
= 4ax(ax2 + b)
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