How to find the derivative of sqrt(x^2+y^2)?

Gaswasserm8o

Gaswasserm8o

Answered question

2023-01-26

How to find the derivative of x 2 + y 2 ?

Answer & Explanation

Kira Ramos

Kira Ramos

Beginner2023-01-27Added 9 answers

d d x ( x ) = 1 2 x , so
d d x ( u ) = 1 2 u d u d x .
d d x ( x 2 + y 2 ) = 1 2 x 2 + y 2 d d x ( x 2 + y 2 )


= 1 2 x 2 + y 2 ( 2 x + 2 y d y d x )
= 1 2 x 2 + y 2 2 x + 1 2 x 2 + y 2 2 y d y d x
= x x 2 + y 2 + y x 2 + y 2 d y d x


In order to solve for d y d x you will, of course, require the remaining derivative from the remaining terms in the initial equation.

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