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Limits and Derivatives — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSLimits and Derivatives1 Mark
Question
For some constants a and b, find the derivative of (ax2 + b)2
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Answer

Here f (x) = (ax2 + b)2 = a2x4 + b2 + 2abx2
$\therefore \;f{\text{'}}(x) = \frac{d}{{dx}}[{a^2}{x^4} + {b^2} + 2ab{x^2}]$
$ = {a^2}\frac{d}{{dx}}({x^4}) + \frac{d}{{dx}}({b^2}) + 2ab\frac{d}{{dx}}({x^2})$
= a2 × 4x3 + 0 + 2ab × 2x
= 4a2x3 + 4abx
= 4ax(ax2 + b)

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