Calculus Examples

Find the Derivative - d/d@VAR F(x) = square root of x-5 cube root of x
Step 1
By the Sum Rule, the derivative of with respect to is .
Step 2
Evaluate .
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Step 2.1
Use to rewrite as .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
To write as a fraction with a common denominator, multiply by .
Step 2.4
Combine and .
Step 2.5
Combine the numerators over the common denominator.
Step 2.6
Simplify the numerator.
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Step 2.6.1
Multiply by .
Step 2.6.2
Subtract from .
Step 2.7
Move the negative in front of the fraction.
Step 3
Evaluate .
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Step 3.1
Use to rewrite as .
Step 3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
Differentiate using the Power Rule which states that is where .
Step 3.4
To write as a fraction with a common denominator, multiply by .
Step 3.5
Combine and .
Step 3.6
Combine the numerators over the common denominator.
Step 3.7
Simplify the numerator.
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Step 3.7.1
Multiply by .
Step 3.7.2
Subtract from .
Step 3.8
Move the negative in front of the fraction.
Step 3.9
Combine and .
Step 3.10
Combine and .
Step 3.11
Move to the denominator using the negative exponent rule .
Step 3.12
Move the negative in front of the fraction.
Step 4
Simplify.
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Step 4.1
Rewrite the expression using the negative exponent rule .
Step 4.2
Multiply by .