# Calculus Examples

,

Consider the function used to find the linearization at .

Substitute the value of into the linearization function.

Replace the variable with in the expression.

Simplify the result.

Add and .

The final answer is .

Find the derivative.

By the Sum Rule, the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Since is constant with respect to , the derivative of with respect to is .

Add and .

Replace the variable with in the expression.

Substitute the components into the linearization function in order to find the linearization at .

Multiply by .

Subtract from .