   Chapter 14, Problem 13RE Mathematical Applications for the ...

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

Solutions

Chapter
Section Mathematical Applications for the ...

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

Find the partial derivative of f ( x ,   y ) =   4 x 3 − 5 x y 2 +   x y 3 with respect to x at the point ( 1 ,   2 ,   – 8 ) .

To determine

To calculate: The partial derivative of the function f(x,y)=4x35xy2+y3 with respect to x at the point (1,2,8).

Explanation

Given Information:

The provided function is f(x,y)=4x35xy2+y3.

The provided point is (1,2,8).

Formula used:

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

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).

Calculation:

Consider the provided function, f(x,y)=4x35xy2+y3

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