What is the derivative of f(x) = ln(sinx))f(x)=ln(sinx))?

2 Answers
Apr 22, 2018

f'(x)=cotx

Explanation:

We'll apply the Chain Rule, which, when applied to logarithms, tells us that if u is some function in terms of x, then

d/dxlnu=1/u*(du)/dx

Here, we see u=sinx, so

f'(x)=1/sinx*d/dxsinx

f'(x)=cosx/sinx

f'(x)=cotx

Apr 22, 2018

f'(x)=cotx

Explanation:

"differentiate using the "color(blue)"chain rule"

"Given "f(x)=g(h(x))" then"

f'(x)=g'(h(x))xxh'(x)larrcolor(blue)"chain rule"

"here "f(x)=ln(sinx)

rArrf'(x)=1/sinx xxd/dx(sinx)=cosx/sinx=cotx