Find the Derivative - d/d@VAR f(x)=2x^2+3x-2

Problem

d()/d(x)*(2*x2+3*x−2)

Solution

1. Identify the function to be differentiated, which is a polynomial ƒ(x)=2*x2+3*x−2

2. Apply the power rule to the first term 2*x2 which states that d(xn)/d(x)=n*x(n−1)

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

3. Apply the power rule to the second term 3*x

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

4. Apply the constant rule to the third term −2 which states that the derivative of a constant is zero.

d(2)/d(x)=0

5. Combine the results of the individual derivatives to find the total derivative of the function.

d(ƒ(x))/d(x)=4*x+3

Final Answer

d(2*x2+3*x−2)/d(x)=4*x+3

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