Calculus Examples

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 .
Since is constant with respect to , the derivative of with respect to is .
Add and to get .
Set the derivative equal to then solve for .
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Rewrite as a set of linear factors.
Divide each term by and simplify.
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Divide each term in by .
Simplify the left side of the equation by cancelling the common factors.
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Multiply by to get .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by to get .
Divide by to get .
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Substitute the values of which cause the derivative to be into the original function.
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Simplify each term.
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Remove parentheses around .
Raising to any positive power yields .
Subtract from to get .
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Since there are no values of where the derivative is undefined, there are no additional critical points.
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