derivatives involving square roots

**Evan.Kimia** · October 31st 2009, 06:11 PM

Find f '(a).

f(x) = √5x + 1

I Know i can turn it into (5x+1)^.5 but im lost from here on out.
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**ramiee2010** · October 31st 2009, 06:21 PM

Originally Posted by Evan.Kimia

Find f '(a).

f(x) = √5x + 1

I Know i can turn it into (5x+1)^.5 but im lost from here on out.
__________________________________________________ ___

is it $f(x)=\sqrt {5x}+1 \quad or \quad f(x)=\sqrt {5} {x}+1$ ?

**Evan.Kimia** · October 31st 2009, 06:24 PM

the square root covers that whole function.

**ramiee2010** · October 31st 2009, 06:38 PM

$f(x)=\sqrt{(5x+1)}$

use chain rule

$f'(x)=\frac{d}{dx}f(x)=\frac{d{f(x)}}{dt} \cdot \frac{dt}{dx}$

assume t=5 x+1
so that f(x)= $t^{\frac{1}{2}}$

if stuck see spoiler

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