de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

taylor ln(cos(x)+sin(x))

Lösung

taylor

ln (cos (x) + sin (x))

Lösung

x - x^{2} + \frac{2}{3} x^{3} - \frac{2}{3} x^{4} + \frac{2}{3} x^{5} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( ln ( cos ( x ) + sin ( x ) ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( cos ( x ) + sin ( x ) ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( cos ( x ) + sin ( x ) ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{4}{3 !} x^{3} + \frac{- 16}{4 !} x^{4} + \frac{80}{5 !} x^{5} + \dots

Fasse zusammen

= x - x^{2} + \frac{2}{3} x^{3} - \frac{2}{3} x^{4} + \frac{2}{3} x^{5} + \dots

Beliebte Beispiele

derivative e^x(x+1)

integral of e^{-5}

derivative of sqrt(x^2-y^2)

integral of 2/(2x-3)

(dy)/(dx)=2y+x^2+5