Find the Derivative - d/d@VAR f(x)=x^2-2x^3

Problem

d()/d(x)*(x^2−2*x^3)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=x^2−2*x^3

2. Apply the sum rule for derivatives, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

3. Apply the power rule to each term, where d(x^n)/d(x)=n*x^(n−1)

4. Differentiate the first term x^2 to get 2*x

5. Differentiate the second term −2*x^3 by multiplying the exponent by the coefficient to get −6*x^2

6. Combine the results to find the final derivative.

Final Answer

d()/d(x)*(x^2−2*x^3)=2*x−6*x^2

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