Differential calc..product rule
1. Let f(x) = e^nx, where n is a positive integer. Find f'(x) (Hint: use the Product Rule)
Okay, it says to use the product rule, thats d/dx = f'g +g'f
I put it as
f'(x) = (ne^nx)g(x) + g'(x)(e^nx)
Im not sure if thats right...because it does not give the g(x), it is there someway to figure it out?
2. Let f1, f2, f3, and f4 be differentiable functions
(a) Find d/dx [f1(x)f2(x)f3(x)]
okay so what i did was, I applied the quotient rule and wrote the above as
= f'g -g'f/g^2
= [f1f2]'[1/f3] - [f'3/f3^2][f1f2]/(1/f3)^2
Is that correct????
(b) Find d/dx [f1(x)f2(x)f3(x)f4(x)]
I basically did what I have done above, and used the product rule
f'(x) = (f1f2)'(f3f4) + (f3f4)'(f1f2)
Anyhelp would be appreciated, thanks guys