derivative sin(log_{10}(1+x))

Lösung

ableitung von

sin (lo g_{10} (1 + x))

\frac{cos ( lo g _{10} ( 1 + x ) )}{ln ( 10 ) ( 1 + x )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

cos (lo g_{10} (1 + x)) \frac{1}{ln ( 10 ) ( 1 + x )} : \frac{cos ( lo g _{10} ( 1 + x ) )}{ln ( 10 ) ( 1 + x )}

= \frac{cos ( lo g _{10} ( 1 + x ) )}{ln ( 10 ) ( 1 + x )}

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

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

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

d er i v a t i v e (x - 1)^{3} (x + 1)^{2}

d er i v a t i v e 6 (x^{2} + 3)^{- 1}