How do you find the derivative of $\sqrt{5 x + 2}$ $sqrt (5x+2)$ ?

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How do you find the derivative of $\sqrt{5 x + 2}$ $sqrt (5x+2)$ ?

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Answer 1 · 2016-01-31T22:46:25

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

Explanation:

rewrite as ${(5 x + 2)}^{\frac{1}{2}}$ $(5x+2)^(1/2)$

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

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

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

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

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How do you find the derivative of $\sqrt{5 x + 2}$ $sqrt (5x+2)$ ?

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How do you find the derivative of √5x+2sqrt (5x+2)?

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How do you find the derivative of $\sqrt{5 x + 2}$ $sqrt (5x+2)$ ?