derivative of 1/(log_{10(x)})

Lösung

\frac{d}{d x} (\frac{1}{lo g _{10} ( x )})

- \frac{1}{ln ( 10 ) x lo g _{10} ( x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{lo g _{10} ( x )})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} (lo g_{10} (x)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( lo g _{10} ( x ) ) ^{2}} \frac{d}{d x} (lo g_{10} (x))

= - \frac{1}{( lo g _{10} ( x ) ) ^{2}} \frac{d}{d x} (lo g_{10} (x))

\frac{d}{d x} (lo g_{10} (x)) = \frac{1}{x ln ( 10 )}

= - \frac{1}{( lo g _{10} ( x ) ) ^{2}} \cdot \frac{1}{x ln ( 10 )}

Vereinfache

- \frac{1}{lo g _{10} ( x ) ^{2}} \cdot \frac{1}{x ln ( 10 )} : - \frac{1}{ln ( 10 ) x lo g _{10} ( x ) ^{2}}

= - \frac{1}{ln ( 10 ) x lo g _{10} ( x ) ^{2}}

\frac{\partial}{\partial y} (4 x^{3} y^{3} - 1)

\int \frac{4 + x + x ^{2}}{x} d x

y^{^{'}} = - \frac{y}{100}, y (0) = 80

\frac{d}{d x} (\frac{2}{cos ( x )})

\frac{d}{d x} (1 0^{x} + 10 x)