taylor (2^k)/(3k)x^k

Lösung

taylor

\frac{2 ^{k}}{3 k} x^{k}

\dots

Schritte zur Lösung

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( \frac{2 ^{k}}{3 k} x ^{k} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{2 ^{k}}{3 k} x ^{k} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{2 ^{k}}{3 k} x ^{k} ) ( 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{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Fasse zusammen

= \dots

\frac{d}{d x} (3 a^{2} x)

d er i v a t i v e q x + r

d er i v a t i v e f (x) = - \frac{18}{x ^{3}}

d er i v a t i v e ln (6 x)

\frac{d y}{d x} + \frac{y}{x} = 3 x^{3} y^{2}