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

Problem

d()/d(x)*(x3−3*x+1)

Solution

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

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

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

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

4. Apply the power rule to the second term, −3*x

(d(−)*3*x)/d(x)=−3

5. Apply the constant rule to the third term, 1 which states the derivative of a constant is 0

d(1)/d(x)=0

6. Combine the results of the individual derivatives to find the final expression.

Final Answer

(d(x3)−3*x+1)/d(x)=3*x2−3

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