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Beliebt Rechnen >

taylor xsin(x^3)

Lösung

taylor

x sin (x^{3})

Lösung

x^{4} - \frac{1}{6} x^{10} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{24}{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{- 604800}{10 !} x^{10} + \dots

Fasse zusammen

= x^{4} - \frac{1}{6} x^{10} + \dots

Beliebte Beispiele

derivative x^{-2/4}+x^{2/4}

integral from 0 to 1 of 1/((x-1)^{2/3)}

derivative of (8x^{1/3})

integral of-cos(t)sin^2(t)

derivative of (e^x/(e^x+5))