Differentiate the function f(x) = ln(cos(6x))?

Question

Differentiate the function f(x) = ln(cos(6x)).

Answer 1

ln(cos(6x))

Remember the derivative of ln = f'(x)/f(x)
the derivative of cos f(x) = -sin f(x) * f'(x)

= [-sin (6x) . 6] / [cos (6x)]

= - 6.sin(6x) / cos (6x)

= -6.tan(6x) -------- remember sin.(f(x))/cos.(f(x)) = tan.(f(x))

Answer 2

We diferentiate this function by the chain rule...



f'(x)=(1/cos(6x))* (derivative of ln)
(-sin(6x))* (derivative of cos)
(6) (derivative of 6x)

= -6*tan(6x)

Answer 3

Let y = ln(cos 6x)
Let u =cos 6x
du/dx = - 6sin 6x and dy/du = 1/u = 1 / (cos 6x)
dy/dx = dy/du x du/dx
dy/dx = (1 / cos(6x)) x (- 6 sin 6x)
dy/dx = - 6 tan 6x

Answer 4

easy one all u have to know is:
ln(u) ' = u'/u where u is a function of x
cos(u) ' = - u' sin(u)

now,applying these we have:
ln(cos(6x)) ' = (cos(6x)) ' / cos(6x)
= -6 sin(6x) / cos6x
= -6 tan(6x)

Coclusion: next time check ur course instead of wasting ur time on the net !!! yo it's direct application

Answer 5

d/dx(ln cos 6x)
= 1/cos 6x d/dx cos 6x
= 1/cos 6x )(- sin 6x) d/dx (6x)
= - 6 tan 6x

Answer 6

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