maclaurin e^{8x}

Lösung

maclaurin

e^{8 x}

1 + 8 x + 32 x^{2} + \frac{256}{3} x^{3} + \frac{512}{3} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( e ^{8 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{8 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{8 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{8}{1 !} x + \frac{64}{2 !} x^{2} + \frac{512}{3 !} x^{3} + \frac{4096}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + 8 x + 32 x^{2} + \frac{256}{3} x^{3} + \frac{512}{3} x^{4} + \dots

s l o p e (- 2, - 2), (- 1, 2)

\frac{\partial}{\partial x} (e^{x^{2} - y^{2} + 4 y})

\int_{1}^{4} (x^{2} - 2) d x

\int \frac{1}{x ^{2} ( x - 1 ) ^{2}} d x

\frac{d}{d x} (3 x^{5} - 30 x^{3})