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 .
Set the derivative equal to .
Solve for .
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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 .
Divide by .
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
Simplify .
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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.
Evaluate.
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Raising to any positive power yields .
Subtract from .
Find the domain of the derivative.
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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.
Interval Notation:
Set-Builder Notation:
Since there are no values of where the derivative is undefined, there are no additional critical points.
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