Find the Derivative - d/dx 1/((1-2x)^3)

Problem

d()/d(x)1/((1−2*x)3)

Solution

1. Rewrite the expression using a negative exponent to prepare for the power rule.

1/((1−2*x)3)=(1−2*x)(−3)

2. Apply the power rule by bringing the exponent down as a coefficient and subtracting one from the exponent.

d(1−2*x)/d(x)=−3*(1−2*x)(−4)⋅d(1−2*x)/d(x)

3. Apply the chain rule by multiplying by the derivative of the inner function 1−2*x

d(1−2*x)/d(x)=−2

4. Multiply the constants together to simplify the expression.

−3⋅−2=6

5. Simplify the final expression by moving the term with the negative exponent back to the denominator.

6*(1−2*x)(−4)=6/((1−2*x)4)

Final Answer

d()/d(x)1/((1−2*x)3)=6/((1−2*x)4)

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