# Equation of the Tangent Line using Differentials

• Feb 20th 2013, 02:00 PM
michellederz
Equation of the Tangent Line using Differentials
Find the equation of the tangent line at the point (-1 , -8)

x2/3-y2/3-5y=37

I keep getting this as the answer which is wrong: y+1=(1/7)(x+8)

Can anyone help me solve this equation? Thank you!

Here is the work I did:
• Feb 20th 2013, 02:50 PM
Plato
Re: Equation of the Tangent Line using Differentials
Quote:

Originally Posted by michellederz
Find the equation of the tangent line at the point (-1 , -8)
x2/3-y2/3-5y=37

$\tfrac{2}{3}x^{-1/3}-\tfrac{2}{3}y^{-1/3}y'-5y'=0$

or $y'=\frac{2x^{-1/3}}{2y^{-1/3}+15}$