Calculus Examples

Find the Derivative Using Quotient Rule - d/dx 1/(x^3)
Step 1
Differentiate using the Quotient Rule which states that is where and .
Step 2
Differentiate.
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Step 2.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 3
Simplify.
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Step 3.1
Simplify the numerator.
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Step 3.1.1
Simplify each term.
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Step 3.1.1.1
Multiply by .
Step 3.1.1.2
Multiply by .
Step 3.1.1.3
Multiply by .
Step 3.1.2
Subtract from .
Step 3.2
Combine terms.
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Step 3.2.1
Multiply the exponents in .
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Step 3.2.1.1
Apply the power rule and multiply exponents, .
Step 3.2.1.2
Multiply by .
Step 3.2.2
Cancel the common factor of and .
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Step 3.2.2.1
Factor out of .
Step 3.2.2.2
Cancel the common factors.
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Step 3.2.2.2.1
Factor out of .
Step 3.2.2.2.2
Cancel the common factor.
Step 3.2.2.2.3
Rewrite the expression.
Step 3.2.3
Move the negative in front of the fraction.