Calculus Qustion

Question

What is the derivative of 2xy-17=-3x²? Is it -y/x-3?

Answer 1

Don,

 

It looks like you tried implicit differentiation.

 

2xy - 17 = -3x²

 

2y + 2xy' = -6x

 

y' = (-6x - 2y)/(2x) = -3 - y/x

 

Note you have a y in the answer, so the solution is not complete.  Use the method in Philip's solution, which I might add, was already used to find this same derivative in a previous posting.

Answer 2

Using implicit differentiation, YES!

 

If you need it all in x's and not both x and y, will get dy/dx = -(3/2) - 17/(2x²) 

Answer 3

First, put the equation into standard form:

 

2xy-17=-3x²

2xy = -3x² + 17

y = -3x/2 + (17/2)x^-1

 

dy/dx = -3/2 - (17/2)x^-2 = -3/2 - 17/(2x²)