maclaurin 10^x

Lösung

maclaurin

1 0^{x}

1 + ln (10) x + \frac{ln ^{2} ( 10 )}{2} x^{2} + \frac{ln ^{3} ( 10 )}{6} x^{3} + \frac{ln ^{4} ( 10 )}{24} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{ln ( 10 )}{1 !} x + \frac{ln ^{2} ( 10 )}{2 !} x^{2} + \frac{ln ^{3} ( 10 )}{3 !} x^{3} + \frac{ln ^{4} ( 10 )}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + ln (10) x + \frac{ln ^{2} ( 10 )}{2} x^{2} + \frac{ln ^{3} ( 10 )}{6} x^{3} + \frac{ln ^{4} ( 10 )}{24} x^{4} + \dots

\frac{d}{d x} (in (x + 3))

\frac{d}{d x} (1 - sin (2 x))

\frac{\partial}{\partial x} (\frac{7 x}{3 y})

n or ma l f (x) = \frac{x}{2 x - 3}, (1, - 1)

f (x) = 14400 + 600 x + x^{2}