Find the Derivative - d/dx 2x^3+3x^2-12x+1

Problem

d()/d(x)*(2*x3+3*x2−12*x+1)

Solution

1. Apply the sum rule for derivatives, which allows for the differentiation of each term in the polynomial individually.

(d(2)*x3)/d(x)+(d(3)*x2)/d(x)−(d(12)*x)/d(x)+d(1)/d(x)

2. Apply the power rule d(xn)/d(x)=n*x(n−1) and the constant multiple rule to the variable terms.

2*(3*x2)+3*(2*x)−12*(1)

3. Apply the constant rule to the last term, noting that the derivative of any constant is 0

d(1)/d(x)=0

4. Simplify the coefficients by performing the multiplication.

6*x2+6*x−12

Final Answer

d()/d(x)*(2*x3+3*x2−12*x+1)=6*x2+6*x−12

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