Question

Find the derivation of 3x² with respect to x using the first principle

Answer 1

because it asks to use *first principle* you will need to calculate this limit

\[\frac{ dy }{ dx }=\lim_{h \rightarrow 0}(\frac{ f(x+h)-f(x) }{ h })\]

basically, you'll calculate f(x+h) by plugging in x + h as your new x-value the function 3x^2
next, you'll subtract f(x+h) - f(x)
you should be able to factor out h when you're done simplifying the numerator f(x+h) - f(x), and thus cancel out the h in the denominator

finally, to take the limit as h --> 0, plug in h = 0

lmk if you're getting stuck with any of these steps, or want to check your answer

Answer 2

Tread carefully.

Let's set h = 0 right from the start [your "plug in h = 0 "].

So:

\(f'(x) = \dfrac{f(x + 0 ) - f(x)}{0} = \dfrac{0}{0}\)

That's Snake Oil.

--> LIMITS

Answer 3

Thanks