Chapter 14, Problem 6RE

### 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

# Find ∂ z ∂ y  if  z = 12 x 5 − 14 x 3 y 3 + 6 y 4 − 1 .

To determine

To calculate: The partial derivative zy of the function z=12x514x3y3+6y41.

Explanation

Given Information:

The provided function is z=12x5âˆ’14x3y3+6y4âˆ’1.

Formula used:

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

Power of x rule for a real number n is such that, if f(x)=xn then fâ€²(x)=nxnâˆ’1.

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).

Calculation:

Consider the provided function, z=12x5âˆ’14x3y3+6y4âˆ’1

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