Find the Derivative - d/dx (2x-3)^4

Problem

d(2*x−3)/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is u4 and the inner function is u=2*x−3

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

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

3. Differentiate the inner function 2*x−3 with respect to x

d(2*x−3)/d(x)=2

4. Multiply the results together to find the final derivative.

4*(2*x−3)3⋅2=8*(2*x−3)3

Final Answer

d(2*x−3)/d(x)=8*(2*x−3)3

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