(\partial)/(\partial x)(ysqrt(x)-y^2-x+3y)

Lösung

\frac{\partial}{\partial x} (y x - y^{2} - x + 3 y)

\frac{y}{2 x} - 1

Schritte zur Lösung

\frac{\partial}{\partial x} (y x - y^{2} - x + 3 y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (y x) - \frac{\partial}{\partial x} (y^{2}) - \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (3 y)

\frac{\partial}{\partial x} (y x) = \frac{y}{2 x}

\frac{\partial}{\partial x} (y^{2}) = 0

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

\frac{\partial}{\partial x} (3 y) = 0

= \frac{y}{2 x} - 0 - 1 + 0

Vereinfache

= \frac{y}{2 x} - 1

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

x \to - 1 + lim (arcsin (x))

\frac{d}{d x} ((4 x + 5)^{2})

f (x) = sin (x^{3})

\int \frac{1}{5 - 7 x - 3 x ^{2}} d x