Find the Derivative - d/dx 2x^2+3x-2

Problem

d()/d(x)*(2*x2+3*x−2)

Solution

1. Apply the sum rule for derivatives, which allows for the differentiation of each term in the expression individually.

(d(2)*x2)/d(x)+(d(3)*x)/d(x)−d(2)/d(x)

2. Apply the power rule to the first term, where d(xn)/d(x)=n*x(n−1)

(d(2)*x2)/d(x)=2⋅2*x(2−1)=4*x

3. Apply the power rule to the second term.

(d(3)*x)/d(x)=3⋅1*x(1−1)=3

4. Apply the constant rule to the third term, noting that the derivative of any constant is zero.

d(2)/d(x)=0

5. Combine the results of the individual derivatives to find the final expression.

4*x+3−0=4*x+3

Final Answer

d()/d(x)*(2*x2+3*x−2)=4*x+3

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