Find the Derivative - d/dx y=8x-x^2

Problem

d()/d(x)*(8*x−x2)

Solution

1. Identify the expression to be differentiated, which is a polynomial consisting of two terms: 8*x and −x2

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

d()/d(x)*(8*x−x2)=(d(8)*x)/d(x)−d(x2)/d(x)

3. Apply the power rule to each term. For any term a*xn the derivative is n⋅a*x(n−1)

(d(8)*x)/d(x)=8

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

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

d(y)/d(x)=8−2*x

Final Answer

d()/d(x)*(8*x−x2)=8−2*x

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