y-f-x-dy-dx-

Question Number 204689 by Davidtim last updated on 25/Feb/24

y =∣ f (x) ∣; \frac{d y}{d x} = ?

Answered by A5T last updated on 25/Feb/24

y = \sqrt{{(f (x))}^{2}} = {[{(f (x))}^{2}]}^{\frac{1}{2}}

\Rightarrow \frac{d y}{d x} = \frac{1}{2 \sqrt{{(f (x))}^{2}}} \times 2 f (x) \times f^{'} (x) = \frac{f (x) f^{^{'}} (x)}{∣ f (x) ∣}

= s g n (f (x)) f^{'} (x)

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