derivative of 6^xlog_{3}(x)

Lösung

\frac{d}{d x} (6^{x} lo g_{3} (x))

\frac{6 ^{x} + ln ( 6 ) \cdot 6 ^{x} x ln ( x )}{ln ( 3 ) x}

Schritte zur Lösung

\frac{d}{d x} (6^{x} lo g_{3} (x))

Wende die Produktregel an:

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

f = 6^{x}, g = lo g_{3} (x)

= \frac{d}{d x} (6^{x}) lo g_{3} (x) + \frac{d}{d x} (lo g_{3} (x)) 6^{x}

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

\frac{d}{d x} (lo g_{3} (x)) = \frac{1}{x ln ( 3 )}

= 6^{x} ln (6) lo g_{3} (x) + \frac{1}{x ln ( 3 )} \cdot 6^{x}

Vereinfache

6^{x} ln (6) lo g_{3} (x) + \frac{1}{x ln ( 3 )} \cdot 6^{x} : \frac{6 ^{x} + ln ( 6 ) \cdot 6 ^{x} x ln ( x )}{ln ( 3 ) x}

= \frac{6 ^{x} + ln ( 6 ) \cdot 6 ^{x} x ln ( x )}{ln ( 3 ) x}

d er i v a t i v e y = (6 x^{2} - 10 x + 1)^{- 4}

\int [\frac{( sin ( x ) )}{x}] d x

\frac{d y}{d x} + x y = 4 x

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