How do you implicitly differentiate #15=x^2-y^2/x#?

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Answer 1 · 2016-03-04T00:42:48

See the explanation section, below.

First of all, I would rewrite the equation. (Why use the quotient rule when we don't need to?)

#15x=x^3-y^2# #" "# (for #x != 0#)

Now differentiate:

#d/dx(15x)=d/dx(x^3) - d/dx(y^2)#

#15=3x^2-2y dy/dx#

Solve for #dy/dx#

#2ydy/dx=3x^2-15#

So, #dy/dx = (3x^2-15)/(2y)#