Ableitung von f(x) = 3·ln(sin(x)/x)

Question

$$3*ln(\frac { sin(x) }{ x } )$$

ich wäre über Hilfe mit erklärung sehr dankbar!

Answer 1

f(x) = 3·LN(SIN(x)/x)

f'(x) = 3/(SIN(x)/x) * (COS(x)*x - SIN(x))/x^2

f'(x) = 3*x/SIN(x) * (COS(x)*x - SIN(x))/x^2

f'(x) = 3/SIN(x) * (COS(x)*x - SIN(x))/x

f'(x) = (3·COS(x)·x - 3·SIN(x)) / (SIN(x)·x)

f'(x) = 3·COS(x)·x / (SIN(x)·x) - 3·SIN(x) / (SIN(x)·x)

f'(x) = 3·COT(x) - 3 / x

Answer 2

f(x)=3*ln(sin(x)/x)=3*ln(sin(x))-3*ln(x)

f'(x)=3*cos(x)/sin(x)-3/x=3*cot(x)-3/x