derivative log_{10}(x^2+3)

Lösung

ableitung von

lo g_{10} (x^{2} + 3)

\frac{2 x}{ln ( 10 ) ( x ^{2} + 3 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{10} (x^{2} + 3))

Wende die log Regel an:

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

= \frac{d}{d x} (\frac{ln ( x ^{2} + 3 )}{ln ( 10 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (x^{2} + 3))

Wende die Kettenregel an:

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

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

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

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{2} + 3} \cdot 2 x

Vereinfache

\frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{2} + 3} \cdot 2 x : \frac{2 x}{ln ( 10 ) ( x ^{2} + 3 )}

= \frac{2 x}{ln ( 10 ) ( x ^{2} + 3 )}

d er i v a t i v e 9.1 1^{x}

d er i v a t i v e x^{x} (lo g_{10} (x) + 1)

d er i v a t i v e f (x) = x^{5} + x^{2} - 2 x + 1

\frac{d}{d t} (2 t (\frac{n}{4}) + c)

d er i v a t i v e ln (tan (\frac{x}{2}))