derivative of ln((7x^{ln(2x)}))

Lösung

\frac{d}{d x} (ln ((7 x)^{l n (2 x)}))

\frac{2 ^{l n (7 x)} x ^{l n (\frac{7}{2}) - 1} ln ( 14 x ^{2} )}{7 ^{l n (2 x)}}

Schritte zur Lösung

\frac{d}{d x} (ln ((7 x)^{l n (2 x)}))

Wende die Kettenregel an:

\frac{1}{( 7 x ) ^{l n (2 x)}} \frac{d}{d x} ((7 x)^{l n (2 x)})

= \frac{1}{( 7 x ) ^{l n (2 x)}} \frac{d}{d x} ((7 x)^{l n (2 x)})

\frac{d}{d x} ((7 x)^{l n (2 x)}) = 2^{l n (7 x)} x^{l n (7 x) - 1} ln (14 x^{2})

= \frac{1}{( 7 x ) ^{l n (2 x)}} \cdot 2^{l n (7 x)} x^{l n (7 x) - 1} ln (14 x^{2})

Vereinfache

\frac{1}{( 7 x ) ^{l n (2 x)}} \cdot 2^{l n (7 x)} x^{l n (7 x) - 1} ln (14 x^{2}) : \frac{2 ^{l n (7 x)} x ^{l n (\frac{7}{2}) - 1} ln ( 14 x ^{2} )}{7 ^{l n (2 x)}}

= \frac{2 ^{l n (7 x)} x ^{l n (\frac{7}{2}) - 1} ln ( 14 x ^{2} )}{7 ^{l n (2 x)}}

\frac{\partial}{\partial z} (8 z e^{x yz})

\frac{d}{d t} (c cos (t) + t^{2} sin (t))

\int \frac{6}{x ^{2} ( x ^{2} + 25 )} d x

x \to 0 lim (x^{2} + x + 1)

e^{x - y} y^{^{'}} = x - 3