   Chapter 14, Problem 14RE

Chapter
Section
Textbook Problem

Find the first partial derivatives.14. g ( u , v ) = u + 2 v u 2 + v 2

To determine

To find: The first order partial derivatives of the function g(u,v)=u+2vu2+v2 .

Explanation

Given:

The function is, g(u,v)=u+2vu2+v2 .

Formula used:

If z=f(x,y) , then the partial derivative functions are,

fx(x,y)=fx=xf(x,y)fy(x,y)=fy=yf(x,y)

Calculation:

Obtain gu(u,v) .

Take the partial derivative of g(u,v) with respect to u.

gu(u,v)=u(u+2vu2+v2)=[(u2+v2)(1+0)(u+2v)(2u)](u2+v2)2=u2+v22u24uv(u2+v2)2=v2u24uv(u2+v2)2

Obtain gv(u,v)

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