Find the Derivative - d/dx f(x)=x-x^3

Problem

d()/d(x)*(x−x^3)

Solution

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

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)*(x−x^3)=d(x)/d(x)−d(x^3)/d(x)

3. Apply the power rule to each term. The power rule states that d(x^n)/d(x)=n*x^(n−1)

d(x)/d(x)=1

d(x^3)/d(x)=3*x^2

4. Combine the results to find the final derivative.

d()/d(x)*(x−x^3)=1−3*x^2

Final Answer

d()/d(x)*(x−x^3)=1−3*x^2

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