Find the Derivative - d/dx y=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 y=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 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 and the constant multiple rule to the second term −3*x2

(d(−)*3*x2)/d(x)=−3*(2*x)=−6*x

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*x2+1)=3*x2−6*x

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