Calculus Examples

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Find the first derivative and evaluate at and to find the slope of the tangent line.
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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.
Simplify and combine like terms.
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Simplify each term.
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Multiply by .
Move to the left of .
Multiply by .
Add and .
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 .
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 .
Evaluate the derivative at .
Simplify.
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Multiply by .
Add and .
Plug the slope and point values into the point-slope formula and solve for .
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Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .
Simplify the equation and keep it in point-slope form.
Solve for .
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Simplify .
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Apply the distributive property.
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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