derivative of (log_{3}(x)/(log_{7)(x)})

Lösung

\frac{d}{d x} (\frac{lo g _{3} ( x )}{lo g _{7} ( x )})

0

Schritte zur Lösung

\frac{d}{d x} (\frac{lo g _{3} ( x )}{lo g _{7} ( x )})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( lo g _{3} ( x ) ) lo g _{7} ( x ) - \frac{d}{d x} ( lo g _{7} ( x ) ) lo g _{3} ( x )}{( lo g _{7} ( x ) ) ^{2}}

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

\frac{d}{d x} (lo g_{7} (x)) = \frac{1}{x ln ( 7 )}

= \frac{\frac{1}{x l n ( 3 )} lo g _{7} ( x ) - \frac{1}{x l n ( 7 )} lo g _{3} ( x )}{( lo g _{7} ( x ) ) ^{2}}

Vereinfache

\frac{\frac{1}{x l n ( 3 )} lo g _{7} ( x ) - \frac{1}{x l n ( 7 )} lo g _{3} ( x )}{lo g _{7} ( x ) ^{2}} : 0

= 0

\int x^{2} - cos (x) d x

d x + e^{5 x} d y = 0

l a pl a ce t r an s f or m s^{2} + 2 s + 1

d er i v a t i v e y = x^{2} e^{x} - 2 x e^{x} + 4 e^{x}

\int (x - π) sin (x) d x