Find the Derivative - d/dx y=(4x-1)^3

Problem

d()/d(x)*(4*x−1)3

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is u3 and the inner function is u=4*x−1

2. Apply the Power Rule to the outer function by bringing the exponent to the front and subtracting one from the power.

3*(4*x−1)(3−1)

3. Multiply by the derivative of the inner function 4*x−1 according to the Chain Rule.

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

4. Differentiate the inner expression 4*x−1 which results in 4

d(4*x−1)/d(x)=3*(4*x−1)2⋅4

5. Simplify the expression by multiplying the constants 3 and 4

d(4*x−1)/d(x)=12*(4*x−1)2

Final Answer

d(4*x−1)/d(x)=12*(4*x−1)2

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