Find the Derivative - d/dx y=(2x+3)^2

Problem

d()/d(x)*(2*x+3)2

Solution

1. Identify the rule needed to differentiate the expression, which is the power rule combined with the chain rule for a function of the form un

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

d(2*x+3)/d(x)=2*(2*x+3)(2−1)⋅d(2*x+3)/d(x)

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

d(2*x+3)/d(x)=2

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

d(2*x+3)/d(x)=2*(2*x+3)1⋅2

5. Simplify the expression by multiplying the constants.

d(2*x+3)/d(x)=4*(2*x+3)

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

d(2*x+3)/d(x)=8*x+12

Final Answer

d(2*x+3)/d(x)=8*x+12

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