Chapter 14, Problem 6T

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Let f ( x , y ) = 2 e x 2 y 2 . Find ∂ 2 f ∂ x ∂ y .

To determine

To calculate: The second partial derivative 2fxy of the function f(x,y)=2ex2y2.

Explanation

Given Information:

The provided function is f(x,y)=2ex2y2.

Formula used:

For a function z(x,y), the second partial derivative, when first derivative is taken with respect to y and second derivative is taken with respect to x is zyx=2zxy=x(zy).

Power of x rule for a real number n is such that, if f(x)=xn then f(x)=nxn1.

Derivative of exponential function is such that, if y=eu, where u is a differentiable function of x then dydx=eududx.

Chain rule for function f(x)=u(v(x)) is f(x)=u(v(x))v(x).

Product rule for function f(x)=u(x)v(x), where u and v are differentiable functions of x, then f(x)=v(x)u(x)+u(x)v(x).

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x)

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