Find the Derivative - d/dx x^3-1

Problem

d()/d(x)*(x3−1)

Solution

1. Identify the expression as a difference of two terms, x3 and 1

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

d()/d(x)*(x3−1)=d(x3)/d(x)−d(1)/d(x)

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

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

4. Apply the constant rule to the second term, where the derivative of any constant is 0

d(1)/d(x)=0

5. Combine the results to find the final derivative.

3*x2−0=3*x2

Final Answer

d()/d(x)*(x3−1)=3*x2

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