Find the Derivative - d/dx x^2(1-5x)

Problem

d()/d(x)*x^2*(1−5*x)

Solution

1. Distribute the x^2 term into the parentheses to simplify the expression before differentiating.

x^2*(1−5*x)=x^2−5*x^3

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

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

(d(5)*x^3)/d(x)=15*x^2

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

d()/d(x)*(x^2−5*x^3)=2*x−15*x^2

Final Answer

d()/d(x)*x^2*(1−5*x)=2*x−15*x^2

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