(\partial)/(\partial x)(xln(x+3y))

Lösung

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

ln (x + 3 y) + \frac{x}{x + 3 y}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = ln (x + 3 y)

= \frac{\partial}{\partial x} (x) ln (x + 3 y) + \frac{\partial}{\partial x} (ln (x + 3 y)) x

\frac{\partial}{\partial x} (x) = 1

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

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

Vereinfache

1 \cdot ln (x + 3 y) + \frac{1}{x + 3 y} x : ln (x + 3 y) + \frac{x}{x + 3 y}

= ln (x + 3 y) + \frac{x}{x + 3 y}

\int \frac{- 4}{3 x ^{2}} d x

x \to 3 lim (\frac{x - 1}{3 - x})

d er i v a t i v e x^{y} + 1

f (x) = e^{2 x} - x^{2} - 1

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