Question

Знайти похідну функцій

 

1)y=lnsinx 

2)y=lncosx

3)y=lntgx 

4)lnctgx 

Answer 1

1) y = lnsinx

$y' = (lnsinx)' = frac{1}{sinx}*sin'x = frac{cosx}{sinx} = ctgx$

2) y = lncosx

$y' = (lncosx)' = frac{1}{cosx}*cos'x =- frac{sinx}{cosx} = - tgx$

3) y = lntgx

$y' = (lntgx)' = frac{1}{tgx}*tg'x = frac{cosx}{sinx}*frac{1}{cos^2x} = frac{1}{sinx*cosx}$

4) y = lnctgx

$y' = (lnctgx)' = frac{1}{ctgx}*ctg'x = frac{sinx}{cosx}*(-frac{1}{sin^2x}) = - frac{1}{sinx*cosx}$