derivative of (3x+1ln(x-1))

Lösung

\frac{d}{d x} ((3 x + 1) ln (x - 1))

3 ln (x - 1) + \frac{3 x + 1}{x - 1}

Schritte zur Lösung

\frac{d}{d x} ((3 x + 1) ln (x - 1))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3 x + 1, g = ln (x - 1)

= \frac{d}{d x} (3 x + 1) ln (x - 1) + \frac{d}{d x} (ln (x - 1)) (3 x + 1)

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

\frac{d}{d x} (ln (x - 1)) = \frac{1}{x - 1}

= 3 ln (x - 1) + \frac{1}{x - 1} (3 x + 1)

\frac{1}{x - 1} (3 x + 1) = \frac{3 x + 1}{x - 1}

= 3 ln (x - 1) + \frac{3 x + 1}{x - 1}

\frac{d}{d x} ((4 x - 7)^{3})

\int_{- π}^{π} x cos (n x) d x

\int \frac{5 e ^{\frac{6}{x ^{4}}}}{x ^{5}} d x

\frac{\partial}{\partial y} (y + sin (\frac{x}{y}))

t an g e n t y = \frac{∣ x ∣}{2 - x ^{2}}, (1, 1)