James Stewart

ISBN: 9781305266643

Textbook Problem

Find the first partial derivatives of the function.

15. f(x, y) = x⁴ + 5xy³

To determine

To find: The first order partial derivatives of the function f(x,y)=x4+5xy3 .

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, f(x,y)=x4+5xy3 (1)

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

fx(x,y)=∂∂x(x4+5xy3)=∂∂x(x4)+∂∂x(5xy3)

Check out a sample textbook solution.

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Find the first partial derivatives of the function. 15. f(x, y) = x4 + 5xy3

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Math
Calculus Multivariable Calculus 8th Edition

Find the first partial derivatives of the function.

15. f(x, y) = x⁴ + 5xy³