# How do you use implicit differentiation to find the slope of the curve given x^2+y^2=25 at (3,-4)?

Sep 24, 2016

I found: $\frac{3}{4}$

#### Explanation:

We first differentiate (implicitly) remembering that $y$ itself will represent a function of $x$ so in differentiating it we need to include this information writing a $\frac{\mathrm{dy}}{\mathrm{dx}}$ term.
So we have:
$2 x + 2 y \frac{\mathrm{dy}}{\mathrm{dx}} = 0$
rearrange:
$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{x}{y}$

This expression will represent the inclination/slope $m$ of your function.

Considering your point we substitute $x = 3 \mathmr{and} y = - 4$ to find the specific slope at that point:
$m = \frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{3}{- 4} = \frac{3}{4}$