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Beliebt Rechnen >

derivative of xln(y+sin(3x))

Lösung

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

Lösung

ln (y) + \frac{x \frac{d y}{d x}}{y} + cos (3 x) \cdot 3

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

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

Beliebte Beispiele

sum from n=1 to infinity of (10/17)^n

n = 1 \sum \infty (\frac{10}{17})^{n}

(\partial)/(\partial x)(cos(xy)y)

\frac{\partial}{\partial x} (cos (x y) y)

derivative of sin^{cos(x}(x))

\frac{d}{d x} (sin^{c o s (x)} (x))

integral of xsin(x)+1

\int x sin (x) + 1 d x

integral from 2 to 4 of (x-2)

\int_{2}^{4} (x - 2) d x