Consider the difference quotient formula.

Evaluate the function at .

Replace the variable with in the expression.

Simplify the result.

Use the Binomial Theorem.

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Remove parentheses.

The final answer is .

Reorder.

Move .

Move .

Move .

Move .

Reorder and .

Find the components of the definition.

Plug in the components.

Simplify the numerator.

Multiply by .

Subtract from .

Add and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Simplify terms.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Move .

Move .

Reorder and .

Find [f(x+h)-f(x)]/h f(x)=6x^3