Calculus Examples

Check if Differentiable Over an Interval
,
Find the derivative.
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Find the first derivative.
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Rewrite as .
Differentiate using the Power Rule which states that is where .
Rewrite the expression using the negative exponent rule .
The first derivative of with respect to is .
Find if the derivative is continuous on .
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To find whether the function is continuous on or not, find the domain of .
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Set the denominator in equal to to find where the expression is undefined.
Solve for .
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Take the square 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.
Plus or minus is .
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
is continuous on .
The function is continuous.
The function is continuous.
The function is differentiable on because the derivative is continuous on .
The function is differentiable.
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