Find the Derivative - d/dx f(x)=(7x+8)^2

Problem

d()/d(x)*(7*x+8)2

Solution

1. Identify the rule needed for the derivative. Since the expression is a function raised to a power, 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 exponent by 1

2*(7*x+8)(2−1)

3. Apply the Chain Rule by multiplying the result by the derivative of the inner function 7*x+8

d(7*x+8)/d(x)=7

4. Combine the results of the previous steps.

2*(7*x+8)1⋅7

5. Simplify the expression by multiplying the constants 2 and 7

14*(7*x+8)

6. Distribute the constant 14 into the binomial.

98*x+112

Final Answer

d(7*x+8)/d(x)=98*x+112

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