Find the Derivative - d/dx y=2x^2-3x

Problem

d()/d(x)*(2*x2−3*x)

Solution

1. Identify the expression as a polynomial consisting of two terms, 2*x2 and −3*x

2. Apply the sum rule for derivatives, which allows for the differentiation of each term independently.

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

4. Calculate the derivative of the first term.

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

5. Apply the power rule to the second term, −3*x noting that the derivative of x is 1

6. Calculate the derivative of the second term.

(d(−)*3*x)/d(x)=−3

7. 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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