   Chapter 14, Problem 16RE

Chapter
Section
Textbook Problem

Find the first partial derivatives.16. G(x, y, z) = exz sin(y/z)

To determine

To find: The first order partial derivatives of the function G(x,y,z)=exzsin(yz) .

Explanation

Given:

The function is, G(x,y,z)=exzsin(yz) .

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 Gx(x,y,z) .

Take the partial derivative of G(x,y,z) with respect to x.

Gx(x,y,z)=x(exzsin(yz))=sin(yz)x(exz)=sin(yz)[exz(z)]=zexzsin(yz)

Obtain Gy(x,y,z) .

Take the partial derivative of G(x,y,z) with respect to y

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