if f(x)= ae^kx and f'(x)/f(x)= -5/2 then k=
Help lol (Relearning calculus and basic rules :P )

Question

if f(x)= ae^kx and f'(x)/f(x)= -5/2 then k= 
Help lol (Relearning calculus and basic rules :P )

bahrom7893 · Answer

find the derivative of f(x):
f'(x) = a*e^(kx)*k (Chain rule)

bahrom7893 · Answer

f'(x) = a*k*e^(kx)
f'(x)/f(x) = -5/2, so
a*k*e^(kx)/[a*e^(kx)] = -5/2

anonymous · Answer

$$f(x)=ae ^{kx}$$$$f'(x)=ake ^{kx}$$reaplce:$$\frac{ake ^{kx}}{ae ^{kx}}=-\frac{5}{2}$$$$k=-\frac{5}{2}$$

bahrom7893 · Answer

a*e^(kx) on top and bottom cancel out, so u're left with k = -5/2

anonymous · Answer

remember:
$$f(x)=e ^{u} $$$$f \prime(x)=e ^{u}u \prime$$

liizzyliizz · Answer

O.o This is so simple lol I am embarrassed I got this wrong now :(

anonymous · Answer

dont forget, click good answer :D jeje

liizzyliizz · Answer

lol there you go :) Thanks for the help.