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Chain Rule of Differentiation

If fx=x|x|, t...

Question

If $f (x) = x | x |$ , then the value of $f^{'} (x) - 2 | x |$ at $x = 2021$ is

A

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B

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C

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Solution

We have,
$f (x) = x | x |$
$\Rightarrow f (x) = {\begin{matrix} - x^{2} x < 0 x^{2} x \geq 0 \end{matrix}$

$\Rightarrow f^{'} (x) = {\begin{matrix} - 2 x x < 0 2 x x \geq 0 \end{matrix}$

$\Rightarrow f^{'} (x) = 2 | x |$
$∴ f^{'} (x) - 2 | x | = 0$
$∴$ at $x = 2021, f^{'} (x) - 2 | x | = 0$

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Chain Rule of Differentiation

Standard XII Mathematics

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