maclaurin f(x)=e^{8x}

Lösung

maclaurin

f (x) = 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

d er i v a t i v e arctan (x y)

\frac{d}{d x} (x^{3} + 7)

\int \frac{144 - x ^{2}}{x} d x

\frac{d}{d x} (3 x^{2} - 6 x + 9)

\frac{\partial}{\partial x} (y - \frac{216}{x ^{2}})