d/(dn)((log_{10}(n))^3)

Lösung

\frac{d}{d n} ((lo g_{10} (n))^{3})

\frac{3 lo g _{10} ( n ) ^{2}}{ln ( 10 ) n}

Schritte zur Lösung

\frac{d}{d n} ((lo g_{10} (n))^{3})

Wende die Kettenregel an:

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

= 3 (lo g_{10} (n))^{2} \frac{d}{d n} (lo g_{10} (n))

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

= 3 (lo g_{10} (n))^{2} \frac{1}{n ln ( 10 )}

Vereinfache

3 lo g_{10} (n)^{2} \frac{1}{n ln ( 10 )} : \frac{3 lo g _{10} ( n ) ^{2}}{ln ( 10 ) n}

= \frac{3 lo g _{10} ( n ) ^{2}}{ln ( 10 ) n}

\int \frac{1}{y ( 2 - y )} d y

d er i v a t i v e f (x) = ln (\frac{1 - x}{1 + x})

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

\int x (3 x^{2} - 7)^{- 2} d x

\frac{d}{d x} (cos^{2} (2 - x^{2}))