derivative of e^{sqrt(xy)}

Lösung

\frac{d}{d x} (e^{x y})

\frac{e ^{x y} ( y + x \frac{d y}{d x} )}{2 x y}

Schritte zur Lösung

\frac{d}{d x} (e^{x y})

Wende die Kettenregel an:

e^{x y} \frac{d}{d x} (x y)

= e^{x y} \frac{d}{d x} (x y)

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

= e^{x y} \frac{y + x \frac{d y}{d x}}{2 x y}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\frac{d}{d x} (csc (x) - cot (x))

\int (18 x + 4) (9 x^{2} + 4 x)^{5} d x

\frac{\partial}{\partial x} (- 4 y^{5} sin (4 x))

\frac{\partial}{\partial x} (7 x^{5} y^{7} + 3 x^{8} y^{6})

t an g e n t f (x) = 4 (x - \frac{1}{x})^{4}, at x = 2