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

Problem

d()/d(x)*(2*x2−3*x)

Solution

1. Identify the function ƒ(x)=2*x2−3*x and apply the sum rule for derivatives, which allows for differentiating each term separately.

2. Apply the power rule to the first term 2*x2 by multiplying the coefficient by the exponent and decreasing the exponent by one.

(d(2)*x2)/d(x)=2⋅2*x(2−1)=4*x

3. Apply the power rule to the second term −3*x (which is −3*x1 by multiplying the coefficient by the exponent and decreasing the exponent by one.

(d(−)*3*x)/d(x)=−3⋅1*x(1−1)=−3

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

Final Answer

d()/d(x)*(2*x2−3*x)=4*x−3

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