calculus question

Can someone explain to me how a general power rule works?

Question

calculus question

Can someone explain to me how a general power rule works?

empty · Answer

Sure I guess we can start here with the most general case and work down from there:

$$[ f(g(x))]' = f'(g(x)) * g'(x)$$

So what are these, an example might help, we can literally pick anything as long as we can find f(x) and g(x).

In this case, the derivative of this:

$$[(3+x^2)^3]'$$
We can cube it all out and get polynomials but that's annoying, instead we can identify:

$$f(x) = x^3$$$$g(x) =3+x^2$$
check to see that $$f(g(x))= (3+x^2)^3$$

Now it becomes a lot easier, since computing $f'(g(x))$ just means take the derivative of $f(x)$ and plug in $g(x)$.

anonymous · Answer

I'm not sure that I'm following along because the way that I had solved one of my problems was taking the derivative of f(x), plugging in g(x) in and then multiplying that by the derivative of g(x)

empty · Answer

Yeah that's perfect that's what you should be doing

anonymous · Answer

Thanks for your help