derivative of log_{10}(2+sin(x))

Lösung

\frac{d}{d x} (lo g_{10} (2 + sin (x)))

\frac{cos ( x )}{ln ( 10 ) ( 2 + sin ( x ) )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{10} (2 + sin (x)))

Wende die log Regel an:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( 2 + sin ( x ) )}{ln ( 10 )})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (2 + sin (x)))

Wende die Kettenregel an:

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

= \frac{1}{2 + sin ( x )} \frac{d}{d x} (2 + sin (x))

\frac{d}{d x} (2 + sin (x)) = cos (x)

= \frac{1}{ln ( 10 )} \cdot \frac{1}{2 + sin ( x )} cos (x)

Vereinfache

\frac{1}{ln ( 10 )} \cdot \frac{1}{2 + sin ( x )} cos (x) : \frac{cos ( x )}{ln ( 10 ) ( 2 + sin ( x ) )}

= \frac{cos ( x )}{ln ( 10 ) ( 2 + sin ( x ) )}

\frac{\partial}{\partial x} (tan (8 + 2 x^{2} y^{3} z^{2}))

\frac{d}{d x} (x (2 x - 5)^{3})

\int 2 cos (x) sin (x) + \frac{1}{2 x} d x

\int 17 sin^{2} (x) cos^{2} (x) d x

y^{^{'}} - \frac{7}{x} y = \frac{y ^{3}}{x ^{10}}