Answer:
cos(4) f'(sin 4)/f(sin 4) is y' at x=4
Step-by-step explanation:
We can't actually find the numerical value for this without more information.
We are given:
y=ln(f(sin x))
This is equivalent to
e^y=f(sin x)
Differentiate both sides:
y' e^y=cos(x) f'(sin x)
Divide both sides by e^y:
y' =cos(x) f'(sin x)/e^y
Rewrite in terms of x using that e^y=f(sin x):
y' =cos(x) f'(sin x)/f(sin x)
Now replace x with 4:
cos(4) f'(sin 4)/f(sin 4) is y' at x=4
