Find the Derivative - d/dx x^3-12x

Problem

d()/d(x)*(x3−12*x)

Solution

1. Identify the expression as a difference of two terms, which allows the use of the sum/difference rule for derivatives.

2. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1) to the first term x3

d(x3)/d(x)=3*x2

3. Apply the power rule to the second term −12*x noting that the derivative of x is 1

d(−12*x)/d(x)=−12

4. 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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