Let $f(x)=x-6x^{3}$. Then according to the definition of derivative

$f^\prime(x)= \displaystyle \lim_{h\to 0}$

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(Your answer above and the next few answers below will involve the variables $x$ and $h$. We are using h instead of $\Delta x$ because it is easier to type)
We can cancel the common factor from the numerator and denominator leaving the polynomial


Taking the limit of this expression gives us $f'(x) =$