Find the Derivative - d/d@VAR f(x)=x^3-12x

Problem

d()/d(x)*(x3−12*x)

Solution

1. Identify the function to be differentiated, which is a polynomial consisting of two terms: x3 and −12*x

2. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives: d()/d(x)*(ƒ(x)+g(x))=d(ƒ(x))/d(x)+d(g(x))/d(x)

3. Apply the power rule to the first term x3 The power rule states d(xn)/d(x)=n*x(n−1) For n=3 we get 3*x2

4. Apply the constant multiple rule and power rule to the second term −12*x The derivative of a*x is simply a For −12*x we get −12

5. Combine the results of the individual derivatives to find the final expression.

Final Answer

(d(x3)−12*x)/d(x)=3*x2−12

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