Find the Derivative - d/dx y=x^3-3x+1

Problem

d()/d(x)*(x3−3*x+1)

Solution

1. Identify the expression to be differentiated, which is a polynomial consisting of three terms: x3 −3*x and 1

2. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives of each individual term.

3. Apply the power rule to the first term x3 where 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 noting that the derivative of any constant is zero.

d(1)/d(x)=0

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

Final Answer

d()/d(x)*(x3−3*x+1)=3*x2−3

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