derivative of log_{e}(3x^2+7)

Lösung

\frac{d}{d x} (lo g_{e} (3 x^{2} + 7))

\frac{6 x}{3 x ^{2} + 7}

Schritte zur Lösung

\frac{d}{d x} (lo g_{e} (3 x^{2} + 7))

Vereinfache

lo g_{e} (3 x^{2} + 7) : ln (3 x^{2} + 7)

= \frac{d}{d x} (ln (3 x^{2} + 7))

Wende die Kettenregel an:

\frac{1}{3 x ^{2} + 7} \frac{d}{d x} (3 x^{2} + 7)

= \frac{1}{3 x ^{2} + 7} \frac{d}{d x} (3 x^{2} + 7)

\frac{d}{d x} (3 x^{2} + 7) = 6 x

= \frac{1}{3 x ^{2} + 7} \cdot 6 x

Vereinfache

\frac{1}{3 x ^{2} + 7} \cdot 6 x : \frac{6 x}{3 x ^{2} + 7}

= \frac{6 x}{3 x ^{2} + 7}

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

y (2 x^{2} + 5 x - 3) d y = e^{y} d x

\frac{\partial}{\partial x} (x e^{7 x y})

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

in v erse l a pl a ce \frac{( 3 s e ^{(- 2 s)} )}{4 s ^{2} + 36}