derivative of xe^{xy}+2xy+1/x

Lösung

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

e^{x y} + e^{x y} x (y + x \frac{d y}{d x}) + 2 (y + x \frac{d y}{d x}) - \frac{1}{x ^{2}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

= e^{x y} + e^{x y} x (y + x \frac{d y}{d x}) + 2 (y + x \frac{d y}{d x}) - \frac{1}{x ^{2}}

y^{^{'}} - e^{y} - 2 x e^{y} = 0

d er i v a t i v e y = sin (tan (7 x))

\frac{\partial}{\partial x} (4 x (3 + y)^{- 1})

\int 56 cos (8 x - 5) d x

\int_{0}^{\infty} (x e^{- x}) d x