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

1 Answer
Sep 24, 2016

I found: #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 #(dy)/(dx)# term.
So we have:
#2x+2y(dy)/(dx)=0#
rearrange:
#(dy)/(dx)=-x/y#

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

Considering your point we substitute #x=3 and y=-4# to find the specific slope at that point:
#m=(dy)/(dx)=-3/(-4)=3/4#