find functions of f and g that show that is incorrect:

d f(x) (d/dx)f(x)
-- --- = ---------
dx g(x) (d/dx)g(x)

Question

find functions of f and g that show that is incorrect:

d    f(x)      (d/dx)f(x) 
--  --- = --------- 
dx  g(x)     (d/dx)g(x)

anonymous · Answer

f[x]=sin[x]
g[x]=cos[x]

anonymous · Answer

d/dx sin x = cos x.......................[1]
d/dx cos x =- sin x ....................[2]
[1]/[2] = -cot[x]

$$d/dx (tan x) = sec^2(x)$$

$$sec^2(x) \neq -cot(x) $$

anonymous · Answer

thanks

anonymous · Answer

yeah, that makes sense. cheers, cyter. Which other pair could disprove this?

anonymous · Answer

f[x]=2x
g[x]=3x

f'[x]/g'[x] = 2/3

d/dx(f[x]/gx)= d/dx(2/3) = 0

$$0\neq \frac{2}{3}$$