Find the Derivative - d/d@VAR f(x)=6x^3

Problem

d()/d(x)*6*x3

Solution

1. Identify the function to be differentiated, which is ƒ(x)=6*x3

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

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

4. Multiply the constant 6 by the exponent 3 and subtract 1 from the exponent.

5. Simplify the resulting expression to find the final derivative.

Final Answer

(d(6)*x3)/d(x)=18*x2

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