Chapter 14, Problem 11RE

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 7-12, find z x  and  z y . 11.   z = e x y + y ln x

To determine

To calculate: The partial derivatives zx and zy of the function z=exy+ylnx.

Explanation

Given Information:

The provided function is z=exy+ylnx.

Formula used:

For a function z(x,y), the partial derivative of z with respect to x is calculated by taking the derivative of z(x,y) with respect to x and keeping the other variable y constant. The partial derivative of z with respect to x is denoted by zx and the partial derivative of z with respect to y is denoted by zy.

Derivative of natural logarithmic functions is such that, if y=lnu, where u is a differentiable function of x then dydx=1uâ‹…dudx.

Derivative of exponential function is such that, if y=eu, where u is a differentiable function of x then dydx=euâ‹…dudx.

Chain rule for function f(x)=u(v(x)) is fâ€²(x)=uâ€²(v(x))â‹…vâ€²(x).

Constant function rule for a constant c is such that, if f(x)=c then fâ€²(x)=0.

Coefficient rule for a constant c is such that, if f(x)=câ‹…u(x), where u(x) is a differentiable function of x, then fâ€²(x)=câ‹…uâ€²(x)

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