Let f(x)=cos(lnx). Then f′(x):

Question

Let f(x)=cos(lnx).  Then f′(x):

anonymous · Answer

chain rule for this one

$$f(g(x))'=f'(g(x))\times g'(x)$$

anonymous · Answer

use 
$$f(x)=\cos(x), g(x)=\ln(x)$$ so you have 
$$f(g(x))$$

anonymous · Answer

you got this?

anonymous · Answer

i can write the answer if you like

anonymous · Answer

Let me try to work it out, and see what I get first just so I can know if I am understanding it. Is that okay?

anonymous · Answer

yes of course that is best

anonymous · Answer

I tried and I got confused along the way. Can you tell me the answer now? I want to see how close I was.

anonymous · Answer

ok in english "derivative of the outside function evaluated at the inside function, times the derivative of the inside function"
you have 
$$\cos(\ln(x))$$ derivative of cosine is - sine so start with 
$$-\sin(\ln(x))$$ then multiply by the derivative of $\ln(x)$ which is $\frac{1}{x}$ to get 
$$-\sin(\ln(x))\times \frac{1}{x}=-\frac{\sin(\ln())}{x}$$\]

anonymous · Answer

I was pretty close, just not close enough! Thanks!!