   Chapter 14, Problem 17RE

Chapter
Section
Textbook Problem

Find the first partial derivatives.17. s ( u , v , w ) = u  arctan( v w )

To determine

To find: The first order partial derivatives of the function S(u,v,w)=uarctan(vw) .

Explanation

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:

Let the given function be, S(u,v,w)=uarctan(vw) (1)

Obtain Su(u,v,w) .

Take the partial derivative with respect to u for the equation (1),

Su(u,v,w)=u(uarctan(vw))=arctan(vw)u(u)=arctan(vw)(1)=arctan(vw)

Obtain Sv(u,v,w)

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