`x^2 - y^2 = 25` Find `dy/dx` by implicit differentiation.

Textbook Question

Chapter 2, 2.5 - Problem 2 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given: `x^2-y^2=25`

`2x-2ydy/dx=0`

`-2ydy/dx=-2x`

`dy/dx=(-2x)/(-2y)`

`dy/dx=(x)/(y)`

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kandukurimaths | Student, Graduate | (Level 1) Honors

Posted on

(x+y)(x-y)=25

apply both side derivative of x than we get

(1+dy/dx)(x-y)+(1-dy/dx)(x+y)=0

2x-2y(dy/dx)=0

dy/dx=y/x

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