(\partial)/(\partial x)((10x)/(1+x^2-y))

Lösung

\frac{\partial}{\partial x} (\frac{10 x}{1 + x ^{2} - y})

\frac{10 ( - x ^{2} - y + 1 )}{( 1 + x ^{2} - y ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{10 x}{1 + x ^{2} - y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 10 \frac{\partial}{\partial x} (\frac{x}{1 + x ^{2} - y})

Wende die Quotientenregel an:

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

= 10 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( 1 + x ^{2} - y ) - \frac{\partial}{\partial x} ( 1 + x ^{2} - y ) x}{( 1 + x ^{2} - y ) ^{2}}

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

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

= 10 \cdot \frac{1 \cdot ( 1 + x ^{2} - y ) - 2 xx}{( 1 + x ^{2} - y ) ^{2}}

Vereinfache

10 \cdot \frac{1 \cdot ( 1 + x ^{2} - y ) - 2 xx}{( 1 + x ^{2} - y ) ^{2}} : \frac{10 ( - x ^{2} - y + 1 )}{( 1 + x ^{2} - y ) ^{2}}

= \frac{10 ( - x ^{2} - y + 1 )}{( 1 + x ^{2} - y ) ^{2}}

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

d er i v a t i v e f (x) = 3 x^{2} - 1

\frac{d y}{d x} = x + 6 y, y (0) = 2

t an g e n t f (x) = \frac{4 x + 5}{x - 1}, (2, 13)

a re a 2 x, 2 x