derivative of 3ysqrt(xy)

Lösung

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

\frac{3 ( y y + 3 x \frac{d y}{d x} y )}{2 x}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

f = y, g = x y

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

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

= 3 (\frac{d y}{d x} x y + \frac{y + x \frac{d y}{d x}}{2 x y} y)

Vereinfache

3 (\frac{d y}{d x} x y + \frac{y + x \frac{d y}{d x}}{2 x y} y) : \frac{3 ( y y + 3 x \frac{d y}{d x} y )}{2 x}

= \frac{3 ( y y + 3 x \frac{d y}{d x} y )}{2 x}

\int 5 cos^{3} (3 x) d x

\int_{- \infty}^{1} x e^{x} d x

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

\int_{- 2}^{4} (- x^{2} + 2 x + 8) d x

\frac{d y}{d x} = (sin^{2} (2 x)) (cos^{2} (y))