Find the Derivative - d/d@VAR f(x)=x^3-3x^2+1

Problem

d()/d(x)*(x3−3*x2+1)

Solution

1. Identify the function to be differentiated, which is a polynomial ƒ(x)=x3−3*x2+1

2. Apply the sum rule for derivatives, which allows for the differentiation of each term individually.

3. Apply the power rule, d(xn)/d(x)=n*x(n−1) to the terms x3 and −3*x2

4. Apply the constant rule, d(c)/d(x)=0 to the constant term 1

5. Simplify the resulting expression to find the final derivative.

Final Answer

(d(x3)−3*x2+1)/d(x)=3*x2−6*x

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