Partial derivatives Find the first partial

Chapter 12, Problem 12E

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QUESTION:

Partial derivatives  Find the first partial derivatives of the following functions.

\(g(x, z)=x \ln \left(z^{2}+x^{2}\right)\)

Questions & Answers

QUESTION:

Partial derivatives  Find the first partial derivatives of the following functions.

\(g(x, z)=x \ln \left(z^{2}+x^{2}\right)\)

ANSWER:

Solution 12E

Step 1 of  2:

In this problem we need to find the first partial derivatives of the function  g(x ,z) = x ln(

Given function is : g(x ,z) = x ln(

Now we have to find the partial derivative with  respect to x .So , in this case assume that z is  constant.

 g(x ,z) =  (x ln()

                 =  (x) (ln() )+ xln() , since  (uv) = v (u)+u (v)

                 = 1(ln() +  (), since ln(f(x)) =  f(x).

                 = ln()+ (2 x+ 0) , , C = 0 , c is constant.

                 = ln()+

      Therefore ,  g(x ,z)  = ln()+

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