Calculus Examples

Find the Derivative - d/dv (v^-3+7v^-2)^3
Step 1
Differentiate using the chain rule, which states that is where and .
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Step 1.1
To apply the Chain Rule, set as .
Step 1.2
Differentiate using the Power Rule which states that is where .
Step 1.3
Replace all occurrences of with .
Step 2
Differentiate.
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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
Differentiate using the Power Rule which states that is where .
Step 2.5
Multiply by .
Step 3
Rewrite the expression using the negative exponent rule .
Step 4
Rewrite the expression using the negative exponent rule .
Step 5
Rewrite the expression using the negative exponent rule .
Step 6
Rewrite the expression using the negative exponent rule .
Step 7
Combine terms.
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Step 7.1
Combine and .
Step 7.2
Combine and .
Step 7.3
Move the negative in front of the fraction.
Step 7.4
Combine and .
Step 7.5
Move the negative in front of the fraction.