Calculus Examples

Set as a function of .
Find the derivative.
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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 to get .
Since is constant with respect to , the derivative of with respect to is .
Add and to get .
Set the derivative equal to then solve the equation .
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Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by to get .
Simplify the right side of the equation.
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Divide by to get .
Multiply by to get .
Solve the original function at .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raise to the power of to get .
Multiply by to get .
Simplify by subtracting numbers.
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Subtract from to get .
Subtract from to get .
The final answer is .
The horizontal tangent lines on function are .
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