# Thread: derivatives involving square roots

1. ## derivatives involving square roots

Find f '(a).

f(x) = √5x + 1

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

2. 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 $\displaystyle f(x)=\sqrt {5x}+1 \quad or \quad f(x)=\sqrt {5} {x}+1$ ?

3. the square root covers that whole function.

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

use chain rule

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

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

if stuck see spoiler
Spoiler:

$\displaystyle \frac{d{f(x)}}{dt} = \frac{1}{2} t^{\frac{-1}{2}}=\frac{1}{2 \sqrt {t}}=\frac{1}{2 \sqrt {5 x+1 }}$
$\displaystyle \frac{dt}{dx}=\frac{d{(5 x+1) }}{dx}=5$
$\displaystyle f'(x)=\frac{d{f(x)}}{dt} \cdot \frac{dt}{dx} =\frac{1}{2 \sqrt {5 x+1 }} \cdot 5=\frac{5}{2 \sqrt {5 x+1 }}$