(\partial)/(\partial x)((rx(K(r,x)-x))/(K(r,x)+ax))

Lösung

\frac{\partial}{\partial x} (\frac{r x ( K ( r , x ) - x )}{K ( r , x ) + a x})

r \frac{( 1 \cdot ( K ( r , x ) - x ) + ( \frac{\partial}{\partial x} ( K ( r , x ) ) - 1 ) x ) ( K ( r , x ) + a x ) - ( \frac{\partial}{\partial x} ( K ( r , x ) ) + a ) x ( K ( r , x ) - x )}{( K ( r , x ) + a x ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{r x ( K ( r , x ) - x )}{K ( r , x ) + a x})

Behandle

a, r

als Konstante

Entferne die Konstante:

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

= r \frac{\partial}{\partial x} (\frac{x ( K ( r , x ) - x )}{K ( r , x ) + a x})

Wende die Quotientenregel an:

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

= r \frac{\frac{\partial}{\partial x} ( x ( K ( r , x ) - x ) ) ( K ( r , x ) + a x ) - \frac{\partial}{\partial x} ( K ( r , x ) + a x ) x ( K ( r , x ) - x )}{( K ( r , x ) + a x ) ^{2}}

\frac{\partial}{\partial x} (x (K (r, x) - x)) = 1 \cdot (K (r, x) - x) + (\frac{\partial}{\partial x} (K (r, x)) - 1) x

\frac{\partial}{\partial x} (K (r, x) + a x) = \frac{\partial}{\partial x} (K (r, x)) + a

= r \frac{( 1 \cdot ( K ( r , x ) - x ) + ( \frac{\partial}{\partial x} ( K ( r , x ) ) - 1 ) x ) ( K ( r , x ) + a x ) - ( \frac{\partial}{\partial x} ( K ( r , x ) ) + a ) x ( K ( r , x ) - x )}{( K ( r , x ) + a x ) ^{2}}

f (x) = 3 x^{2} + 1

y^{^{'}} = \frac{( 4 t + y )}{4 y - t}

d er i v a t i v e \frac{e ^{\frac{1}{x}}}{x ^{3}}

t an g e n t f (x) = x + 1, (3, 2)

\int C e^{- a t} d t