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Beliebt Rechnen >

derivative of log_{10}(x/(sqrt(x^2+1)))

Lösung

\frac{d}{d x} (lo g_{10} (\frac{x}{x ^{2} + 1}))

Lösung

\frac{1}{ln ( 10 ) x ( x ^{2} + 1 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{10} (\frac{x}{x ^{2} + 1}))

Wende die log Regel an:

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

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

(\partial)/(\partial x)(sqrt(15-2x^2-y^2))

\frac{\partial}{\partial x} (15 - 2 x^{2} - y^{2})

derivative (3+x^4)^{4/5}

d er i v a t i v e (3 + x^{4})^{\frac{4}{5}}

limit as x approaches 0+of (10)/(x^2)

x \to 0 + lim (\frac{10}{x ^{2}})

derivative f(x)= x/(x+2)

d er i v a t i v e f (x) = \frac{x}{x + 2}

\frac{d y}{d t} = 9 t^{2}