# Derivative: find a slope of tangent line=square root of 4-5x when x=-1 ?

## I want to know which formula will work to find slope in derivative and what will be its answer.

##### 1 Answer
Feb 17, 2018

$m = \frac{- 5}{6}$

#### Explanation:

For square roots, I like to change the notation to exponential notation rather than radical notation:

$\sqrt{4 - 5 x} = {\left(4 - 5 x\right)}^{\frac{1}{2}}$

So now we have

$y = {\left(4 - 5 x\right)}^{\frac{1}{2}}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2} {\left(4 - 5 x\right)}^{- \frac{1}{2}} \cdot \frac{d}{\mathrm{dx}} \left(4 - 5 x\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2} {\left(4 - 5 x\right)}^{- \frac{1}{2}} \cdot \left(- 5\right)$

Change back to radical notation

(dy)/(dx)=(-5)/(2sqrt((4-5x))

Substituting x=-1 gives us

$m = \frac{- 5}{2 \sqrt{\left(4 - 5 \left(- 1\right)\right)}} = \frac{- 5}{2 \sqrt{9}} = \frac{- 5}{6}$