Calculus Examples

Find the Derivative - d/dx 1/((1-2x)^3)
Step 1
Apply basic rules of exponents.
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Step 1.1
Rewrite as .
Step 1.2
Multiply the exponents in .
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Step 1.2.1
Apply the power rule and multiply exponents, .
Step 1.2.2
Multiply by .
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
Differentiate using the Power Rule which states that is where .
Step 2.3
Replace all occurrences of with .
Step 3
Differentiate.
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Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
Add and .
Step 3.4
Since is constant with respect to , the derivative of with respect to is .
Step 3.5
Multiply by .
Step 3.6
Differentiate using the Power Rule which states that is where .
Step 3.7
Multiply by .
Step 4
Rewrite the expression using the negative exponent rule .
Step 5
Simplify.
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Step 5.1
Combine and .
Step 5.2
Reorder terms.