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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding Partial Derivatives In Exercises 41–50, find the first partial derivatives.

w = 3 x y 5 x z 2 + 2 y z

To determine

To calculate: The partial derivative of function w=3xy5xz3+2yz.

Explanation

Given Information:

The provided function is w=3xy5xz3+2yz.

Formula used:

The power rule of differentiation with respect to x by holding y and z constant,

x[f(x,y,z)]n=n[f(x,y,z)]n1xf(x,y,z)

The power rule of differentiation with respect to y by holding x and z constant,

y[f(x,y,z)]n=n[f(x,y,z)]n1yf(x,y,z)

The power rule of differentiation with respect to z by holding x and y constant,

z[f(x,y,z)]n=n[f(x,y,z)]n1zf(x,y,z)

Calculation:

Consider the function,

w=3xy5xz3+2yz

Differentiate with respect to x by holding y constant and z constant,

wx=x(3xy5xz3+2yz)=(3y)x(x)(5z3)x(x)

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