derivative of log_{10}((x-3^2))

Lösung

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

\frac{2}{ln ( 10 ) ( x - 3 )}

Schritte zur Lösung

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

Wende die log Regel an:

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

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{4 x ^{2} + 1}{2 x + 5} d x

\int e^{- \frac{3}{2} t} d t

d er i v a t i v e 3 x^{2} + 4 x + 8

d er i v a t i v e (x^{2} + 7)^{5}

a re a x, x^{3} - x^{2} - x