Find the Derivative - d/dx (4x+5)^2

Problem

d(4*x+5)/d(x)

Solution

1. Identify the rule needed for the derivative, which is the Chain Rule for a function of the form un

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+5)(2−1)

3. Apply the Chain Rule by multiplying by the derivative of the inner function, 4*x+5

d(4*x+5)/d(x)=4

4. Combine the results of the outer and inner derivatives.

2*(4*x+5)1⋅4

5. Simplify the expression by multiplying the constants.

8*(4*x+5)

6. Distribute the constant if necessary to reach the final polynomial form.

32*x+40

Final Answer

d(4*x+5)/d(x)=32*x+40

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