Find the Derivative - d/dx f(x)=x^3-2x

Problem

d()/d(x)*(x3−2*x)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=x3−2*x

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.

3. Apply the power rule to the first term, x3 The power rule d(xn)/d(x)=n*x(n−1) gives 3*x2

4. Apply the power rule to the second term, −2*x The derivative of x is 1 so the result is −2

5. Combine the results to find the final derivative.

Final Answer

(d(x3)−2*x)/d(x)=3*x2−2

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