(\partial)/(\partial x)(f(x,y)(x/y))

Lösung

\frac{\partial}{\partial x} (f (x, y) (\frac{x}{y}))

\frac{1}{y} (\frac{\partial}{\partial x} (f (x, y)) x + 1 \cdot f (x, y))

Schritte zur Lösung

\frac{\partial}{\partial x} (f (x, y) (\frac{x}{y}))

Behandle

y

als Konstante

Entferne die Konstante:

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

= \frac{1}{y} \frac{\partial}{\partial x} (f (x, y) x)

Wende die Produktregel an:

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

f = f (x, y), g = x

= \frac{1}{y} (\frac{\partial}{\partial x} (f (x, y)) x + \frac{\partial}{\partial x} (x) f (x, y))

\frac{\partial}{\partial x} (x) = 1

= \frac{1}{y} (\frac{\partial}{\partial x} (f (x, y)) x + 1 \cdot f (x, y))

\frac{d}{d a} (sin^{2} (a) cos^{2} (a))

y^{^{'}} + y = \frac{1}{1 + e ^{2 x}}

d er i v a t i v e (x^{4} + 3 x^{2}) (1 - 5 x)

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

\int \frac{3 x ^{2} + 2}{x ^{3} + 2 x} d x