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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Find the first partial derivatives.

15. F(α, β) = α2 ln(α2 + β2)

To determine

To find: The first order partial derivatives of the function F(α,β)=α2ln(α2+β2) .

Explanation

Given:

The function is, F(α,β)=α2ln(α2+β2) .

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:

Obtain Fα(α,β) .

Take the partial derivative of F(α,β) with respect to α .

Fα(α,β)=α(α2ln(α2+β2))=[α21(α2+β2)(2α+0)+ln(α2+β2)(2α)]=2α3α2+β2+2αln(α2+β2)

Take the partial derivative of F(α,β) with respect to β

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Chapter 14 Solutions

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