derivative (x^9-x^{1/6})6^x

Lösung

ableitung von

(x^{9} - x^{\frac{1}{6}}) 6^{x}

\frac{6 ^{x - 1} ( - 1 + 54 x ^{\frac{53}{6}} ) + ln ( 6 ) \cdot 6 ^{x} x ^{\frac{59}{6}} - ln ( 6 ) \cdot 6 ^{x} x}{x ^{\frac{5}{6}}}

Schritte zur Lösung

\frac{d}{d x} ((x^{9} - x^{\frac{1}{6}}) \cdot 6^{x})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{9} - x^{\frac{1}{6}}, g = 6^{x}

= \frac{d}{d x} (x^{9} - x^{\frac{1}{6}}) 6^{x} + \frac{d}{d x} (6^{x}) (x^{9} - x^{\frac{1}{6}})

\frac{d}{d x} (x^{9} - x^{\frac{1}{6}}) = \frac{- 1 + 54 x ^{\frac{53}{6}}}{6 x ^{\frac{5}{6}}}

\frac{d}{d x} (6^{x}) = 6^{x} ln (6)

= \frac{- 1 + 54 x ^{\frac{53}{6}}}{6 x ^{\frac{5}{6}}} \cdot 6^{x} + 6^{x} ln (6) (x^{9} - x^{\frac{1}{6}})

Vereinfache

\frac{- 1 + 54 x ^{\frac{53}{6}}}{6 x ^{\frac{5}{6}}} \cdot 6^{x} + 6^{x} ln (6) (x^{9} - x^{\frac{1}{6}}) : \frac{6 ^{x - 1} ( - 1 + 54 x ^{\frac{53}{6}} ) + ln ( 6 ) \cdot 6 ^{x} x ^{\frac{59}{6}} - ln ( 6 ) \cdot 6 ^{x} x}{x ^{\frac{5}{6}}}

= \frac{6 ^{x - 1} ( - 1 + 54 x ^{\frac{53}{6}} ) + ln ( 6 ) \cdot 6 ^{x} x ^{\frac{59}{6}} - ln ( 6 ) \cdot 6 ^{x} x}{x ^{\frac{5}{6}}}

t \to π lim (cos (t))

(ln (sec (x)))^{^{'}}

\int 4 x + sin (3 x) d x

s l o p e in t erce pt (6.4) (2.1)

\frac{\partial}{\partial x} (- 2 e^{- 3 x^{2} - y^{2}} y)