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

Problem

d()/d(x)*(x−2)*(2*x+3)

Solution

1. Expand the expression using the FOIL method to simplify the differentiation process.

(x−2)*(2*x+3)=2*x2+3*x−4*x−6

2. Combine like terms to obtain a polynomial in standard form.

2*x2−x−6

3. Apply the power rule, which states d(xn)/d(x)=n*x(n−1) to each term of the polynomial.

(d(2)*x2)/d(x)=4*x

(d(−)*x)/d(x)=−1

(d(−)*6)/d(x)=0

4. Sum the resulting derivatives to find the final derivative of the expression.

4*x−1

Final Answer

d()/d(x)*(x−2)*(2*x+3)=4*x−1

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