i have no idea how to do this.. If f'(x) = x^3 and u = e^x, show that d/dx(f(u)) = e^4x i dont evne know where to begin...

Yay calculus. First (and you probably know this), f'(x) is shorthand for df/dx so if f'(x) = x^3 then f(x) = (1/4)(x^4) (anti-derivative of x^3) So f(u) = f(e^x)= (1/4)((e^x)^4) = (1/4)(e^4x) d/dx((1/4)(e^4x)) = (1/4) d/dx(e^4x) (Constant rule: If k is constant then d/dx(kx) = k(d/dx(x))) Now apply the chain rule to the new derivative: If h(x) = f(g(x)) then h'(x) = f'(g(x)) g'(x)Letting f(x) = e^xand g(x) = 4xNow derive: f(x) = e^x => f'(x)= e^x (e^x is its own derivative) g(x) = 4x => g'(x) = (4)(1x^0) = 4 So h'(x) = (e^(4x))(4)= 4e^4x So back to d/dx((1/4)(e^4x))= (1/4) d/dx(e^4x) = (1/4) (4e^4x) = (1/4) (4) (e^4x) = e^4x I repeat: yay calculus. And I eagerly await a bulletin board that can handle MathML. Also, I take the title "Pokemon Professor" quite literally.

And I told myself I'd never need this crap again. I was right. But I'm glad I could remember some of it

lol weird. I've just been doing this exact same stuff this week. You guys use slightly different notations to us but its all the same in the end. math <3

Sheesh that's complicated. Why not just say d/dx(f(u)) = f'(u)u' = [(e^x)^3][e^x] = (e^3x)(e^x) = e^4x ? Also, technically, you should probably have a constant at the end of your integral. Even though you're just going to take the derivative immediately.

Honestly, I just missed the fact I could use the chain rule on the original problem. No big deal, the proof still works

I just posted here to see whats going on in this thread.By the way till high standard i had not heard about this chain rule.Which standard do u read?

Because it was a Random "Topic!" On top of that, there are some VERY intelligent people on Pokegym, that have expertises is different areas...The above happened to be in "Math.":thumb:

The first explanation is good because it is far easier to use if the problem had more complicated derivatives... but yes, forgetting constants of integration is a big no-no They give the same answer in the end - use the one you like best.

click here... ^ Is that for you? I'm scared of this kind of stuff when I get to high school..I'm gonna be posting stuff like this on here alot :lol: P.S. is this random or what? the above link was so funny...