Find the Derivative - d/dx f(x)=x^3-8

Problem

d()/d(x)*(x3−8)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=x3−8

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

d()/d(x)*(x3−8)=d(x3)/d(x)−d(8)/d(x)

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

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

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

d(8)/d(x)=0

5. Combine the results to find the final derivative.

3*x2−0=3*x2

Final Answer

d()/d(x)*(x3−8)=3*x2

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