# Thread: Slope of tangeant question

1. ## Slope of tangeant question

Can't figure this out, solve for the derivitive using first principles
2/(x+5)^1/2

2. Originally Posted by Shout
Can't figure this out, solve for the derivitive using first principles
2/(x+5)^1/2
$\displaystyle f(x) = \frac{2}{\sqrt{x+5}}$

$\displaystyle f(x+h) = \frac{2}{\sqrt{(x+h) +5}}$

$\displaystyle f'(x) = \lim_{h \to 0} \frac{1}{h} \left(\frac{2}{\sqrt{(x+h) + 5}} - \frac{2}{\sqrt{x+5}}\right)$

now do the grunt work algebra ... start by combining the two fractions in ( ) , then rationalize the numerator.