maclaurin (1-x)^{-1/2},4

Lösung

maclaurin

(1 - x)^{- \frac{1}{2}}, 4

1 + \frac{1}{2} x + \frac{3}{8} x^{2} + \frac{5}{16} x^{3} + \frac{35}{128} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{\frac{1}{2}}{1 !} x + \frac{\frac{3}{4}}{2 !} x^{2} + \frac{\frac{15}{8}}{3 !} x^{3} + \frac{\frac{105}{16}}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + \frac{1}{2} x + \frac{3}{8} x^{2} + \frac{5}{16} x^{3} + \frac{35}{128} x^{4} + \dots

s l o p e y = x^{2} - 3

f (x) = x sin (\frac{4}{x})

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

a re a x = y^{2}, x = y^{2} + 2

d er i v a t i v e arcsin (cos (x^{3}))