Calculus Examples

Find the Derivative - d/dx natural log of cube root of x
Step 1
Use to rewrite as .
Step 2
Differentiate using the chain rule, which states that is where and .
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Step 2.1
To apply the Chain Rule, set as .
Step 2.2
The derivative of with respect to is .
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate using the Power Rule which states that is where .
Step 4
To write as a fraction with a common denominator, multiply by .
Step 5
Combine and .
Step 6
Combine the numerators over the common denominator.
Step 7
Simplify the numerator.
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Step 7.1
Multiply by .
Step 7.2
Subtract from .
Step 8
Move the negative in front of the fraction.
Step 9
Combine and .
Step 10
Multiply by .
Step 11
Simplify the expression.
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Step 11.1
Move to the left of .
Step 11.2
Move to the denominator using the negative exponent rule .
Step 12
Simplify the denominator.
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Step 12.1
Multiply by by adding the exponents.
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Step 12.1.1
Move .
Step 12.1.2
Use the power rule to combine exponents.
Step 12.1.3
Combine the numerators over the common denominator.
Step 12.1.4
Add and .
Step 12.1.5
Divide by .
Step 12.2
Simplify .