Calculus Examples

Find the Derivative - d/dx x^(1/3)(x^2-4)
Step 1
Differentiate using the Product Rule which states that is where and .
Step 2
Differentiate.
Tap for more steps...
Step 2.1
By the Sum Rule, the derivative of with respect to is .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Since is constant with respect to , the derivative of with respect to is .
Step 2.4
Add and .
Step 3
Multiply by by adding the exponents.
Tap for more steps...
Step 3.1
Move .
Step 3.2
Multiply by .
Tap for more steps...
Step 3.2.1
Raise to the power of .
Step 3.2.2
Use the power rule to combine exponents.
Step 3.3
Write as a fraction with a common denominator.
Step 3.4
Combine the numerators over the common denominator.
Step 3.5
Add and .
Step 4
Move to the left of .
Step 5
Differentiate using the Power Rule which states that is where .
Step 6
To write as a fraction with a common denominator, multiply by .
Step 7
Combine and .
Step 8
Combine the numerators over the common denominator.
Step 9
Simplify the numerator.
Tap for more steps...
Step 9.1
Multiply by .
Step 9.2
Subtract from .
Step 10
Move the negative in front of the fraction.
Step 11
Combine and .
Step 12
Move to the denominator using the negative exponent rule .
Step 13
Simplify.
Tap for more steps...
Step 13.1
Apply the distributive property.
Step 13.2
Combine terms.
Tap for more steps...
Step 13.2.1
Combine and .
Step 13.2.2
Move to the numerator using the negative exponent rule .
Step 13.2.3
Multiply by by adding the exponents.
Tap for more steps...
Step 13.2.3.1
Use the power rule to combine exponents.
Step 13.2.3.2
To write as a fraction with a common denominator, multiply by .
Step 13.2.3.3
Combine and .
Step 13.2.3.4
Combine the numerators over the common denominator.
Step 13.2.3.5
Simplify the numerator.
Tap for more steps...
Step 13.2.3.5.1
Multiply by .
Step 13.2.3.5.2
Subtract from .
Step 13.2.4
Combine and .
Step 13.2.5
Move the negative in front of the fraction.
Step 13.2.6
To write as a fraction with a common denominator, multiply by .
Step 13.2.7
Combine and .
Step 13.2.8
Combine the numerators over the common denominator.
Step 13.2.9
Multiply by .
Step 13.2.10
Add and .