Find the Derivative - d/dx y=2x^2-5x

Problem

d()/d(x)*(2*x2−5*x)

Solution

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

d()/d(x)*(2*x2−5*x)=(d(2)*x2)/d(x)−(d(5)*x)/d(x)

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

(d(2)*x2)/d(x)=2⋅2*x(2−1)=4*x

3. Apply the power rule to the second term, noting that x is x1

(d(5)*x)/d(x)=1⋅5*x(1−1)=5

4. Combine the results to find the final derivative of the function.

d(y)/d(x)=4*x−5

Final Answer

d()/d(x)*(2*x2−5*x)=4*x−5

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