Find the Derivative - d/dx y=6x-x^2

Problem

d()/d(x)*(6*x−x2)

Solution

1. Identify the expression to be differentiated, which is a polynomial consisting of two terms: 6*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(6*x−x2)/d(x)=(d(6)*x)/d(x)−d(x2)/d(x)

3. Apply the power rule to each term, where d(xn)/d(x)=n*x(n−1)

4. Differentiate the first term 6*x to get 6

(d(6)*x)/d(x)=6

5. Differentiate the second term x2 to get 2*x

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

6. Combine the results to find the final derivative.

Final Answer

d(6*x−x2)/d(x)=6−2*x

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