Q:
# How do you find the second partial derivative?

The second partial derivative for a function with two or more variables is found by differentiating twice in terms of one variable or in terms of one variable and then another variable. For instance, a function with the variables x and y has three second partial derivatives, one in terms of x, one in terms of y and one in terms of mixed variables.

Continue ReadingFor the function f(x, y)=(x^2)(y^3), the second partial derivative in terms of x is found by differentiating once in terms of x, and then differentiating the resulting function again in terms of x. The first partial derivative with respect to x is 2x(y^3), as the derivative of x^2 is 2x. The second partial derivative with respect to x is 2(y^3). Again, this derivative is found by differentiating 2x. For the same function, the second partial derivative can also be obtained with respect to the variable y. The first partial derivative with respect to y is 3(x^2)(y^2), while the second partial derivative with respect to y is 6(x^2)y. The second partial derivative of any function with multiple variables can be found using this technique. The first partial derivative with respect to x is written as f_x(x, y), while the second partial derivative with respect to x is written as f_xx(x, y). To find a mixed partial derivative, the function is differentiated first in terms of one variable and then in terms of the other. Regardless of order, the result is the same. For example, the mixed partial derivative of the above function is 6x(y^2).

Learn more about Calculus-
Q:
## How do you explain a gradient vector field in calculus?

A: Lamar University explains that a gradient vector field is a directional derivative that represents the change in the gradient of a function. Gradient field... Full Answer >Filed Under: -
Q:
## What is the derivative of 3x?

A: The derivative of 3x is 3. Whenever a mathematical function is defined by a constant multiplied by x, the derivative of the function equals the constant. T... Full Answer >Filed Under: -
Q:
## What is the derivative of secant squared?

A: The derivative of the function secant squared of x is d/dx(sec^2(x)) = 2sec^2(x)tan(x). This derivative is obtained by applying the chain rule of different... Full Answer >Filed Under: -
Q:
## How do you change an equation from standard form to slope intercept form?

A: First, rearrange the variables so that the y term is on the left side of the equal sign and the remaining terms are on the right side of the equal sign. Ne... Full Answer >Filed Under: