derivative of xln(x+2y)

Lösung

\frac{d}{d x} (x ln (x + 2 y))

ln (x + 2 y) + \frac{x ( 1 + 2 \frac{d y}{d x} )}{x + 2 y}

Schritte zur Lösung

\frac{d}{d x} (x ln (x + 2 y))

Wende die Produktregel an:

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

f = x, g = ln (x + 2 y)

= \frac{d x}{d x} ln (x + 2 y) + \frac{d}{d x} (ln (x + 2 y)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (ln (x + 2 y)) = \frac{1 + 2 \frac{d y}{d x}}{x + 2 y}

= 1 \cdot ln (x + 2 y) + \frac{1 + 2 \frac{d y}{d x}}{x + 2 y} x

Vereinfache

1 \cdot ln (x + 2 y) + \frac{1 + 2 \frac{d y}{d x}}{x + 2 y} x : ln (x + 2 y) + \frac{x ( 1 + 2 \frac{d y}{d x} )}{x + 2 y}

= ln (x + 2 y) + \frac{x ( 1 + 2 \frac{d y}{d x} )}{x + 2 y}

\frac{d}{d t} (t^{3} - t)

\frac{d y}{d x} = x x - 15

in v erse l a pl a ce \frac{6}{s} + 8 a \frac{1}{s ^{2} + 16}

\frac{d}{d x} (- 3 x y)

\frac{d}{d x} y + y = 7