Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

dont forget, click good answer :D jeje

Answer 8

lol there you go :) Thanks for the help.