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forgotten how to differentiate...

In uni now, forgotten my alevel maths. could anyone help with this simple question pls.

differentiate y=ln(cosx)

thanks in advance.
Reply 1
Avatar for elpaw
elpaw
15
y' = -sinx/cosx = -tanx
Reply 2
Avatar for Newton
Newton
By using the Chain rule:

(dy/dx)=((du)/(dx))((dy)/(du))

Let u=cosx => (du/dx)=(-(sinx))

y=lnu => (dy)/(du)=1/u

Therefore:

(dy/dx)=(1/u)(-(sinx))=(1/cos)(-(sinx))=-tanx

Newton.
Newton
By using the Chain rule:

(dy/dx)=((du)/(dx))((dy)/(du))

Let u=cosx => (du/dx)=(-(sinx))

y=lnu => (dy)/(du)=1/u

Therefore:

(dy/dx)=(1/u)(-(sinx))=(1/cos)(-(sinx))=-tanx

Newton.


just remember d/dx [ln (u)] = 1/u * du/dx
in thiis case it is 1/cos x * -sin x - -tan x

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