Find the Derivative - d/dx y=3x-x^2

Problem

d()/d(x)*(3*x−x2)

Solution

1. Identify the expression to be differentiated, which is a polynomial consisting of two terms: 3*x and −x2

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

3. Apply the power rule to the first term, 3*x Since the derivative of x is 1 the derivative is 3(1) = 3$.

4. Apply the power rule to the second term, −x2 The power rule d(xn)/d(x)=n*x(n−1) gives 2*x(2−1)=2*x

5. Combine the results to find the final derivative.

Final Answer

d()/d(x)*(3*x−x2)=3−2*x

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