Find the Derivative - d/dx y=4x-x^2

Problem

d()/d(x)*(4*x−x2)

Solution

1. Identify the expression to be differentiated, which is a polynomial consisting of two terms: 4*x and −x2

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

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

3. Apply the power rule to the first term, where (d(a)*x)/d(x)=a

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

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

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

5. Combine the results to find the final derivative.

d(y)/d(x)=4−2*x

Final Answer

d()/d(x)*(4*x−x2)=4−2*x

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