How do you find the derivative of $f (x) = \frac{1}{\sqrt{x}}$ $f(x) = 1/sqrtx$ ?

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How do you find the derivative of $f (x) = \frac{1}{\sqrt{x}}$ $f(x) = 1/sqrtx$ ?

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Answer 1 · 2016-06-17T18:33:05

Use the chain rule.

Explanation:

$y = \frac{1}{u^{\frac{1}{2}}} = u^{- \frac{1}{2}}$ $y = 1/u^(1/2) = u^(-1/2)$

$u = x$ $u = x$

The chain rule states that $\frac{d y}{d x} = \frac{d y}{d u} \times \frac{d u}{d x}$ $dy/dx = dy/(du) xx (du)/dx$ . We must therefore we must differentiate both $u$ $u$ and $y$ $y$ .

$u' = 1$

$:.y' = -1/2u^(-3/2)$

$y' = -1/(2sqrt(u^3))$

$dy/dx = 1 xx -1/(2sqrt(u^3))$

$dy/dx = -1/(2sqrt(x^3))$

Hopefully this helps!

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How do you find the derivative of $f (x) = \frac{1}{\sqrt{x}}$ $f(x) = 1/sqrtx$ ?

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