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

Problem

d()/d(x)*(4*x−2)2

Solution

1. Identify the rule needed to differentiate the expression. Since the function is in the form un where u=4*x−2 we must use the power rule combined with 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

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

3. Differentiate the inner function 4*x−2 with respect to x

d(4*x−2)/d(x)=4

4. Substitute the derivative of the inner function back into the expression.

d(y)/d(x)=2*(4*x−2)1⋅4

5. Simplify the expression by multiplying the constants 2 and 4

d(y)/d(x)=8*(4*x−2)

6. Distribute the 8 into the binomial to reach the final simplified form.

d(y)/d(x)=32*x−16

Final Answer

d(4*x−2)/d(x)=32*x−16

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