find-n-th-dervaiteve-of-ln-cosx-

Question Number 167357 by mkam last updated on 13/Mar/22

f i n d n^{t h} d e r v a i t e v e o f l n (c o s x) ?

Answered by Coronavirus last updated on 16/Mar/22

p o s o n s f (x) = l n (\cos (x))

\partial f = - \tan (x)

\partial^{2} f = - 1 - \tan^{2} (x)

\partial^{3} f = - 2 \tan (x) - {2 \tan}^{3} (x)

\partial^{4} f = - {4 \tan}^{2} (x) - {6 \tan}^{4} (x) + 2

et omme \tan (x) = \sin (x) \times \frac{1}{\cos (x)}

a p r e s j e p e n s e \overset{`}{a} u t i l i s e r l a f l o r m u l e d e L e i b n i z

\partial^{n} (f . g) = \underset{i = 0}{\sum^{n}} C_{n}^{i} (\partial^{i} f^{}) (\partial^{n - i} g)