What is the derivative of $\sqrt{5 x + 2}$ $sqrt(5x+2)$ ?

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What is the derivative of $\sqrt{5 x + 2}$ $sqrt(5x+2)$ ?

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Answer 1 · 2016-10-24T19:25:59

$\frac{5}{2 \sqrt{5 x + 2}}$ $5/(2sqrt(5x+2))$

Explanation:

differentiate using the $chain rule$ $color(blue)"chain rule"$

$\sqrt{5 x + 2} = {(5 x + 2)}^{\frac{1}{2}}$ $sqrt(5x+2)=(5x+2)^(1/2)$

$\frac{d}{d x} {(5 x + 2)}^{\frac{1}{2}} = \frac{1}{2} {(5 x + 2)}^{- \frac{1}{2}} . \frac{d}{d x} (5 x + 2)$ $d/dx(5x+2)^(1/2)=1/2(5x+2)^(-1/2).d/dx(5x+2)$

$= \frac{5}{2} {(5 x + 2)}^{- \frac{1}{2}} = \frac{5}{2 {(5 x + 2)}^{\frac{1}{2}}} = \frac{5}{2 \sqrt{5 x + 2}}$ $=5/2(5x+2)^(-1/2)=5/(2(5x+2)^(1/2))=5/(2sqrt(5x+2))$

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What is the derivative of $\sqrt{5 x + 2}$ $sqrt(5x+2)$ ?

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