Find the derivative of $f (x) = (x^{3} - 2 x)^{2}$

6 x^{5} - 12 x^{3} + 8 x

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6 x^{5} - 16 x^{3} + 8 x

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x^{6} - 4 x^{4} + 4 x^{2}

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6 x^{5} - 16 x^{3} - 8 x

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Solution

The correct option is B $6 x^{5} - 16 x^{3} + 8 x$
$f (x) = (x^{3} - 2 x)^{2}$
$= (x^{3})^{2} + (- 2 x)^{2} - 2 (x^{3}) (2 x)$
$= x^{6} + 4 x^{2} - 4 x^{4}$
Derivative of $f (x)$ is given by
$f^{'} (x) = 6 x^{5} + 4 \times 2 x - 4 \times 4 x^{3}$
$= 6 x^{5} - 16 x^{3} + 8 x$

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