Calculus Examples

,
Find and evaluate at and to find the slope of the tangent line at and .
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Simplify .
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Rewrite as .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Remove parentheses.
Simplify and combine like terms.
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Simplify each term.
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Multiply by by adding the exponents.
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Combine and
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Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Move to the left of the expression .
Multiply by .
Multiply by .
Add and .
Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
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By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Evaluate .
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Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Since is constant with respect to , the derivative of with respect to is .
Add and .
Reform the equation by setting the left side equal to the right side.
Replace with .
Evaluate at .
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Replace the variable with in the expression.
Multiply by .
Add and .
Plug in the slope of the tangent line and the and values of the point into the point-slope formula .
Simplify.
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The slope-intercept form is , where is the slope and is the y-intercept.
Rewrite in slope-intercept form.
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Simplify .
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Simplify the expression.
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Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Move all terms not containing to the right side of the equation.
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Add to both sides of the equation.
Add and .
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