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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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In Exercises 20-23, find the first partial derivatives and evaluate each at the point ( 2 ,   3 ) .

f ( x , y ) = x 3 e 2 y

To determine

To calculate: The first partial derivatives of the given function with respect to x and y respectively and evaluate that values at the given point (2,3) and equation of the function fx(x,y)=3x2e2y.

Explanation

Given Information:

The equation of the function fx(x,y)=3x2e2y and the point is (2,3).

Formula used:

Step 1: Write the given function.

Step 2: Find the first order partial derivative with respect to x using the primary equation.

Step 3: Find the first order partial derivative with respect to y using the secondary equation.

Step 4: To find the value of partial derivative of the given function with respect to x at the Point (x1,y1) replace x by x1 and y by y1 in the equation of partial derivative with respect to x.

Step 5: To find the value of partial derivative of the function with respect to y at the (x1,y1) replace x by x1 and y by y1 in the equation of partial derivative with respect to y.

Calculation:

Consider the given equation

f(x,y)=x3e2y

Now, differentiate given equation with respect to x.

fx(x,y)=3x2e2y …… (1)

Now, differentiate given equation with respect to y.

fy(x,y)=x3ddy(e2y)fy(x,y)=x3e2yddy(2y)fy(x,y)=x3e2y

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