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Home  >>  CBSE XI  >>  Math  >>  Limits and Derivatives
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For some constants $a$ and $b$, find the derivative of \[\] $ (ax^2+b)^2$

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Let $f(x) = (ax^2+b)^2$
$ \Rightarrow f(x) =a^2x^4+2abx^2+b^2$
$ \therefore f'(x) = \large\frac{d}{dx}$$(a^2x^4+2abx^2+b^2) =a^2\large\frac{d}{dx}$$(x^4)+2ab\large\frac{d}{dx}$$(x^2)+\large\frac{d}{dx}$$(b^2)$
On using theorem $\large\frac{d}{dx} $$(x^n)=nx^{n-1}$, we obtain
$f'(x) = a^2(4x^3)+2ab(2x)+b^2(0)$
$ = 4a^2x^3+4abx$
$ = 4ax(ax^2+b)$
answered Apr 9, 2014 by thanvigandhi_1

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