Chapter 14, Problem 5RE

### 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 ∂ x  if  z = 5 x 3 + 6 x y + y 2 .

To determine

To calculate: The partial derivative zx of the function z=5x3+6xy+y2.

Explanation

Given Information:

The provided function is z=5x3+6xy+y2.

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.

Power of x rule for a real number n is such that, if f(x)=xn then f(x)=nxn1.

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

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x)

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