How do you find the derivative of #x^2 - y^2 = 16#?

1 Answer
May 26, 2015

I assume that we want to find #dy/dx#

#x^2 - y^2 = 16#

Our choices are: solve for #y# (make the function(s) explicit and differentiate

OR

leave the function #=f(x)# implicit and use implicit differentiation.

Because this question was posted under Implicit Differentiation, we'll do that.

#x^2 - y^2 = 16#
so the derivative with respect to #x# of the left side equals the derivative with respect to #x# of the right.

We write:

#d/dx(x^2 - y^2) = d/dx(16)#

Now find the derivatives (remembering that #y# is some unknown function of #x#, so we need the chain rule to differentiate #y^2#

#2x-2y dy/dx = 0#

Solve for #dy/dx = x/y#