Question

if existent the first derivatives of the following: f(x):= ln(cos(3x))

Answer 1

explanation ???

Answer 2

chain rule, and the known derivatives of ln and cos.

Answer 3

chain rule\[\ln (f(x))'=\frac{ f'(x) }{ f(x) }\]

Answer 4

thanks

Answer 5

any you write the solution step by step? please

Answer 6

Read up on the chain rule. See how it applies to your function.

This is what the chain rule says, basically:

If you have a function f(g(x)), then d/dx f(g(x)) = d/dx f(x) * d/dx g(x).

Answer 7

For example, your function is ln(cos(3x)). That's actually ln(f(x)), where f(x) = cos(3x).

So the derivative is d/dx ln f(x) * d/dx f(x) = 1/(cos(3x)) * d/dx f(x).

This is since d/dx ln x = 1/x. But here, x is actually another function which is f(x).

Then you need to take the derivative of cos(3x).

You really should read the wiki page on the chain rule or something. it'll explain it better. Just read the simple examples.