`e^(x/y) = x - y` Find `(dy/dx)` by implicit differentiation.

Textbook Question

Chapter 3, 3.5 - Problem 15 - Calculus: Early Transcendentals (7th Edition, James Stewart).
See all solutions for this textbook.

1 Answer | Add Yours

embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

FindĀ `(dy)/(dx) ` if `e^(x/y)=x-y ` by implicit differentiation:

Note that if u is a differentiable function of x then `d/(dx)e^u=e^u (du)/(dx) ` .

Then:

`d/(dx) e^(x/y)=d/(dx)(x-y) `

`e^(x/y) d/(dx)(x/y)=1-y' `

` e^(x/y)(y-xy')/y^2=1-y' `

`e^(x/y)y-e^(x/y)xy'=y^2-y^2y' `

`y'(y^2-e^(x/y)x)=y^2-e^(x/y)y `

`y'=(y(y-e^(x/y)))/(y^2-xe^(x/y)) `

We’ve answered 318,932 questions. We can answer yours, too.

Ask a question