I am doing implicit differentiation and I want to know the fastest way to simplify this and find y'. My online algebra calculator fails to ever solve problems the easy way. Hoping a math pro on here could show me "the easy way". (x+y+y′)/(xy)=e^(7x−y)(7−y′) = 1/x+y′/y=7e^(7x−y)−y′e^(7x−y) y′=?

odcinaknr

odcinaknr

Answered question

2022-09-29

I am doing implicit differentiation and I want to know the fastest way to simplify this and find y'. My online algebra calculator fails to ever solve problems the easy way. Hoping a math pro on here could show me "the easy way".
x + y + y x y = e 7 x y ( 7 y )
=
1 x + y y = 7 e 7 x y y e 7 x y
y = ?

Answer & Explanation

Corbin Hanson

Corbin Hanson

Beginner2022-09-30Added 10 answers

multiplying by
x y
we get
x + y + y = x y e 7 x y ( 7 y )
multiplying out:
x + y + y = 7 x y e 7 x y y x y e 7 x y
y + y x y e 7 x y = 7 x y e 7 x y x y
y ( 1 + x y e 7 x y ) = 7 x y e 7 x y x y
therefore
y = 7 x y e 7 x y x y 1 + x y e 7 x y

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?