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

Problem

d()/d(x)*x2*(1−2*x)

Solution

1. Distribute the x2 term into the parentheses to rewrite the function as a polynomial, which simplifies the differentiation process.

ƒ(x)=x2−2*x3

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

d(ƒ(x))/d(x)=d(x2)/d(x)−(d(2)*x3)/d(x)

3. Differentiate the first term, x2 to get 2*x

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

4. Differentiate the second term, 2*x3 by multiplying the exponent by the coefficient to get 6*x2

(d(2)*x3)/d(x)=6*x2

5. Combine the results to find the final derivative.

d(ƒ(x))/d(x)=2*x−6*x2

Final Answer

(d(x2)*(1−2*x))/d(x)=2*x−6*x2

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