Question

Implicit partial derivative calculator.

A) Partial differentiation
B) Linear programming
C) Quadratic regression
D) Logarithmic expression

Answer 1

Partial differentiation is a technique used to find the derivatives of multivariable functions. Implicit partial differentiation refers to finding the partial derivatives of an equation that is defined implicitly, rather than explicitly. This can be done by differentiating both sides of the equation with respect to each variable.

Step-by-step explanation:

A) Partial differentiation is a technique used to find the derivatives of multivariable functions. In the context of calculus, it is used to find the rates at which the function changes with respect to each variable. Implicit partial differentiation refers to finding the partial derivatives of an equation that is defined implicitly, rather than explicitly. This can be done by differentiating both sides of the equation with respect to each variable.

For example, consider the equation x^2 + y^2 = 1. To find the partial derivative of y with respect to x, we differentiate both sides of the equation with respect to x:

2x + 2yy' = 0

Simplifying, we get y' = -x/y.