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

Problem

d()/d(x)*(2*x+5)2

Solution

1. Identify the rule needed for the derivative, which is the Power Rule combined with the Chain Rule for an expression of the form un

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

2*(2*x+5)(2−1)

3. Apply the Chain Rule by multiplying the result by the derivative of the inner function 2*x+5

d(2*x+5)/d(x)=2

4. Combine the parts to find the total derivative.

2*(2*x+5)1⋅2

5. Simplify the expression by multiplying the constants.

4*(2*x+5)

6. Distribute the constant if needed to reach the final simplified form.

8*x+20

Final Answer

d(2*x+5)/d(x)=8*x+20

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