# Math Help - Equation of the Tangent Line using Differentials

1. ## 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:

2. ## Re: Equation of the Tangent Line using Differentials

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