Find dy/dx y=(4x-1)^2

Problem

d()/d(x)*(4*x−1)2

Solution

1. Identify the rule needed to differentiate the expression. Since the function is in the form un we use the chain rule.

2. Apply the power rule to the outer function by bringing the exponent 2 to the front and decreasing the power by 1

2*(4*x−1)(2−1)

3. Apply the chain rule by multiplying the result by the derivative of the inner function 4*x−1

d(4*x−1)/d(x)=4

4. Combine the components to find the derivative.

d(y)/d(x)=2*(4*x−1)⋅4

5. Simplify the expression by multiplying the constants.

d(y)/d(x)=8*(4*x−1)

6. Distribute the constant if desired to reach the final form.

d(y)/d(x)=32*x−8

Final Answer

d(y)/d(x)=32*x−8

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