Find the 2nd Derivative x^3

Problem

d2(x3)/(d(x)2)

Solution

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

2. Apply the power rule for the first derivative, which states d(xn)/d(x)=n*x(n−1)

3. Calculate the first derivative:

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

4. Apply the power rule again to the first derivative to find the second derivative.

5. Calculate the second derivative:

(d(3)*x2)/d(x)=3⋅2*x(2−1)

6. Simplify the resulting expression:

(d(3)*x2)/d(x)=6*x

Final Answer

d2(x3)/(d(x)2)=6*x

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