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

Problem

d()/d(x)*(5*x−x2)

Solution

1. Identify the expression to be differentiated, which is a polynomial consisting of two terms: 5*x and −x2

2. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives.

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

3. Apply the power rule to each term. For 5*x the derivative is 5 For x2 the derivative is 2*x

(d(5)*x)/d(x)=5

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

4. Combine the results to find the final derivative.

d(y)/d(x)=5−2*x

Final Answer

d(5*x−x2)/d(x)=5−2*x

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