maclaurin x^5sin(x)

Lösung

maclaurin

x^{5} sin (x)

x^{6} - \frac{1}{6} x^{8} + \frac{1}{120} x^{10} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( x ^{5} sin ( x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{5} sin ( x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{5} sin ( x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{720}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 6720}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{30240}{10 !} x^{10} + \dots

Fasse zusammen

= x^{6} - \frac{1}{6} x^{8} + \frac{1}{120} x^{10} + \dots

\frac{d}{d x} (\frac{sin ( x )}{cos ^{2} ( x )})

\frac{d}{d x} (4 - x^{\frac{2}{3}})

\frac{d}{d x} (x^{\frac{4}{3}} - 5)

\int_{- 1}^{3} (1 + 4 x) d x

\frac{d}{d x} (3 x^{3} + 5 x)