# Calculus Examples

Find the Difference Quotient
Consider the difference quotient formula. Use this formula to solve for the slope of the secant line .
Find the components of the definition.
Evaluate the function at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Remove parentheses.
Simplify and combine like terms.
Simplify each term.
Use the power rule to combine exponents.
Use the power rule to combine exponents.
Reorder and .
Apply the distributive property.
Multiply by to get .
Remove parentheses around .
Apply the distributive property.
Remove unnecessary parentheses.
Find the components of the definition.
Plug in the components.
Simplify.
Simplify the numerator.
Apply the distributive property.
Simplify.
Move parentheses.
Remove parentheses.
Subtract from to get .
Subtract from to get .
Factor out of .
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Divide by to get .

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