taylor cos(x^2)*2x

Lösung

taylor

cos (x^{2}) \cdot 2 x

2 x - x^{5} + \frac{1}{12} x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{2}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 120}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{30240}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Fasse zusammen

= 2 x - x^{5} + \frac{1}{12} x^{9} + \dots

\int 4 (6 x + 1)^{5} d x

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

\int_{0}^{1} x^{4} e^{8 x} d x

d er i v a t i v e f (x) = (x - 2) (2 x + 3)

d er i v a t i v e f (t) = 3 t^{3} - \frac{2}{t ^{2}}