Calculus Examples

Find the Derivative - d/dx 4 square root of x^3
Step 1
Rewrite as .
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Step 1.1
Factor out .
Step 1.2
Pull terms out from under the radical.
Step 2
Use to rewrite as .
Step 3
Multiply by by adding the exponents.
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Step 3.1
Multiply by .
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Step 3.1.1
Raise to the power of .
Step 3.1.2
Use the power rule to combine exponents.
Step 3.2
Write as a fraction with a common denominator.
Step 3.3
Combine the numerators over the common denominator.
Step 3.4
Add and .
Step 4
Since is constant with respect to , the derivative of with respect to is .
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.
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Step 9.1
Multiply by .
Step 9.2
Subtract from .
Step 10
Combine and .
Step 11
Combine and .
Step 12
Multiply by .
Step 13
Factor out of .
Step 14
Cancel the common factors.
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Step 14.1
Factor out of .
Step 14.2
Cancel the common factor.
Step 14.3
Rewrite the expression.
Step 14.4
Divide by .