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

Problem

d()/d(x)*(x−2)*(2*x+3)

Solution

1. Identify the function h(x)=(x−2)*(2*x+3) and the need to apply the product rule, which states d()/d(x)*ƒ(x)*g(x)=ƒ(x)d(g(x))/d(x)+g(x)d(ƒ(x))/d(x)

2. Assign the parts of the product where ƒ(x)=x−2 and g(x)=2*x+3

3. Differentiate each part individually.

d(x−2)/d(x)=1

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

4. Apply the product rule by substituting the functions and their derivatives into the formula.

h(x)′=(x−2)*(2)+(2*x+3)*(1)

5. Distribute the constants into the binomials.

h(x)′=2*x−4+2*x+3

6. Combine like terms to find the final derivative.

h(x)′=4*x−1

Final Answer

d()/d(x)*(x−2)*(2*x+3)=4*x−1

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