The given function is f(x)=3x3 f(x) = 3x^3 f(x)=3x3. This is a polynomial function, and we need to find its derivative.
The power rule for differentiation states that if f(x)=axn f(x) = ax^n f(x)=axn, then f′(x)=anxn−1 f^{\prime}(x) = anx^{n-1} f′(x)=anxn−1.
Using the power rule, differentiate f(x)=3x3 f(x) = 3x^3 f(x)=3x3:
f′(x)=3⋅3x3−1=9x2 f^{\prime}(x) = 3 \cdot 3x^{3-1} = 9x^2 f′(x)=3⋅3x3−1=9x2
The derivative of the function is:
f′(x)=9x2 \boxed{f^{\prime}(x) = 9x^2} f′(x)=9x2
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