taylor (x^2)/(x^4+16)

Lösung

taylor

\frac{x ^{2}}{x ^{4} + 16}

\frac{1}{16} x^{2} - \frac{1}{256} x^{6} + \frac{4294967296}{1 6 ^{11}} x^{10} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( \frac{x ^{2}}{x ^{4} + 16} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{x ^{2}}{x ^{4} + 16} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{x ^{2}}{x ^{4} + 16} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{\frac{1}{8}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- \frac{45}{16}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{\frac{1.55856 E 16}{1 6 ^{11}}}{10 !} x^{10} + \dots

Fasse zusammen

= \frac{1}{16} x^{2} - \frac{1}{256} x^{6} + \frac{4294967296}{1 6 ^{11}} x^{10} + \dots

\frac{\partial}{\partial x} (y^{8} + 2 x^{6} + 2 x y)

d er i v a t i v e f (x) = 2 x^{3} - 5 x^{2} + 3 x - 7

d er i v a t i v e 3 + 5 cos (3 t)

x \to 6 lim (ln (7 - x))

\frac{\partial}{\partial x} (e^{x} tan (y))