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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

= (y + 3) \frac{1 \cdot ( x ^{2} + y ) - 2 xx}{( x ^{2} + y ) ^{2}}

Vereinfache

(y + 3) \frac{1 \cdot ( x ^{2} + y ) - 2 xx}{( x ^{2} + y ) ^{2}} : \frac{( - x ^{2} + y ) ( y + 3 )}{( x ^{2} + y ) ^{2}}

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

x^{4} e^{y} + (x + 1) y \frac{d y}{d x} = 0

d er i v a t i v e f (x) = (1 + cos^{2} (x))^{6}

\int_{5}^{10} a x - 10 b d x

t an g e n t f (x) = \frac{12}{x}, at x = - 2

\frac{d}{d z} (0)