de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative y=log_{3}(x^2+1)

Lösung

ableitung von

y = lo g_{3} (x^{2} + 1)

Lösung

\frac{2 x}{ln ( 3 ) ( x ^{2} + 1 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{3} (x^{2} + 1))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( x ^{2} + 1 )}{ln ( 3 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (x^{2} + 1))

Wende die Kettenregel an:

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

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

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

= \frac{1}{ln ( 3 )} \cdot \frac{1}{x ^{2} + 1} \cdot 2 x

Vereinfache

\frac{1}{ln ( 3 )} \cdot \frac{1}{x ^{2} + 1} \cdot 2 x : \frac{2 x}{ln ( 3 ) ( x ^{2} + 1 )}

= \frac{2 x}{ln ( 3 ) ( x ^{2} + 1 )}

Graph

Beliebte Beispiele

(dy}{dx}=\frac{26)/x

\frac{d y}{d x} = \frac{26}{x}

derivative f(x)=x^4+9x

d er i v a t i v e f (x) = x^{4} + 9 x

integral of cos(x)sin(y)

\int cos (x) sin (y) d x

limit as x approaches infinity of 4,x

x \to \infty lim (4, x)

(\partial)/(\partial x)(sec^2(2x+3y)*3)

\frac{\partial}{\partial x} (sec^{2} (2 x + 3 y) \cdot 3)