Find the Derivative - d/dx (4x-7)^2

Problem

d()/d(x)*(4*x−7)2

Solution

1. Identify the rule needed for the expression, which is the power rule combined with the chain rule for a function of the form u*(x)n

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

2*(4*x−7)(2−1)

3. Apply the chain rule by multiplying the result by the derivative of the inner function 4*x−7

2*(4*x−7)1⋅d(4*x−7)/d(x)

4. Differentiate the inner function 4*x−7 which results in 4

2*(4*x−7)⋅4

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

8*(4*x−7)

6. Distribute the 8 to reach the final expanded form.

32*x−56

Final Answer

d(4*x−7)/d(x)=32*x−56

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