maclaurin a^x

Lösung

maclaurin

a^{x}

1 + ln (a) x + \frac{ln ^{2} ( a )}{2} x^{2} + \frac{ln ^{3} ( a )}{6} x^{3} + \frac{ln ^{4} ( a )}{24} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{ln ( a )}{1 !} x + \frac{ln ^{2} ( a )}{2 !} x^{2} + \frac{ln ^{3} ( a )}{3 !} x^{3} + \frac{ln ^{4} ( a )}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + ln (a) x + \frac{ln ^{2} ( a )}{2} x^{2} + \frac{ln ^{3} ( a )}{6} x^{3} + \frac{ln ^{4} ( a )}{24} x^{4} + \dots

\frac{\partial}{\partial x} (ln (x^{2} + x))

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

d er i v a t i v e \frac{85 t}{99 t - 85}

x \to 3 lim (x^{2} + 2 x - 1)

v + x \cdot \frac{d v}{d x} = x^{2} - 1 + 2 v