Find the Derivative - d/dx x^2(1-4x)

Problem

d()/d(x)*x2*(1−4*x)

Solution

1. Distribute the x2 term into the parentheses to simplify the expression before differentiating.

x2*(1−4*x)=x2−4*x3

2. Apply the power rule which states that d(xn)/d(x)=n*x(n−1) to each term of the polynomial.

d(x2)/d(x)=2*x

(d(4)*x3)/d(x)=12*x2

3. Combine the results using the sum/difference rule for derivatives.

d()/d(x)*(x2−4*x3)=2*x−12*x2

Final Answer

(d(x2)*(1−4*x))/d(x)=2*x−12*x2

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