(\partial}{\partial x}(\frac{(a{R}(x)+b+c{R}(x)+de+{f}(x)+{g}(x)e))/x)

Lösung

\frac{\partial}{\partial x} (\frac{( a R ( x ) + b + c R ( x ) + d e + f ( x ) + g ( x ) e )}{x})

\frac{a x \frac{\partial}{\partial x} ( R ( x ) ) + c x \frac{\partial}{\partial x} ( R ( x ) ) + x \frac{\partial}{\partial x} ( f ( x ) ) + e x \frac{\partial}{\partial x} ( g ( x ) ) - a R ( x ) - b - c R ( x ) - e d - f ( x ) - e g ( x )}{x ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{( a R ( x ) + b + c R ( x ) + d e + f ( x ) + g ( x ) e )}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{\partial}{\partial x} ( a R ( x ) + b + c R ( x ) + d e + f ( x ) + g ( x ) e ) x - \frac{\partial}{\partial x} ( x ) ( a R ( x ) + b + c R ( x ) + d e + f ( x ) + g ( x ) e )}{x ^{2}}

\frac{\partial}{\partial x} (a R (x) + b + c R (x) + d e + f (x) + g (x) e) = a \frac{\partial}{\partial x} (R (x)) + c \frac{\partial}{\partial x} (R (x)) + \frac{\partial}{\partial x} (f (x)) + e \frac{\partial}{\partial x} (g (x))

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

= \frac{( a \frac{\partial}{\partial x} ( R ( x ) ) + c \frac{\partial}{\partial x} ( R ( x ) ) + \frac{\partial}{\partial x} ( f ( x ) ) + e \frac{\partial}{\partial x} ( g ( x ) ) ) x - 1 \cdot ( a R ( x ) + b + c R ( x ) + d e + f ( x ) + g ( x ) e )}{x ^{2}}

Vereinfache

\frac{( a \frac{\partial}{\partial x} ( R ( x ) ) + c \frac{\partial}{\partial x} ( R ( x ) ) + \frac{\partial}{\partial x} ( f ( x ) ) + e \frac{\partial}{\partial x} ( g ( x ) ) ) x - 1 \cdot ( a R ( x ) + b + c R ( x ) + d e + f ( x ) + g ( x ) e )}{x ^{2}} : \frac{a x \frac{\partial}{\partial x} ( R ( x ) ) + c x \frac{\partial}{\partial x} ( R ( x ) ) + x \frac{\partial}{\partial x} ( f ( x ) ) + e x \frac{\partial}{\partial x} ( g ( x ) ) - a R ( x ) - b - c R ( x ) - e d - f ( x ) - e g ( x )}{x ^{2}}

= \frac{a x \frac{\partial}{\partial x} ( R ( x ) ) + c x \frac{\partial}{\partial x} ( R ( x ) ) + x \frac{\partial}{\partial x} ( f ( x ) ) + e x \frac{\partial}{\partial x} ( g ( x ) ) - a R ( x ) - b - c R ( x ) - e d - f ( x ) - e g ( x )}{x ^{2}}

\int 12 x^{5} d x

\int_{0}^{5} ∣ 2 x - 5 ∣ d x

\frac{d}{d x} (2 x + 6)

\frac{\partial}{\partial x} (4 e^{x y})

a re a y = x, y = 4, x = 0, x = 22