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

Problem

d()/d(x)*(−2*x3)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=−2*x3

2. Apply the constant multiple rule, which states that d()/d(x)*[c⋅g(x)]=c⋅d(g(x))/d(x)

3. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1)

4. Multiply the constant coefficient by the result of the power rule.

(d(−)*2*x3)/d(x)=−2⋅3*x(3−1)

5. Simplify the expression to find the final derivative.

(d(−)*2*x3)/d(x)=−6*x2

Final Answer

(d(−)*2*x3)/d(x)=−6*x2

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