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Beliebt Rechnen >

(\partial}{\partial x}(\frac{h(x)c)/x)

Lösung

\frac{\partial}{\partial x} (\frac{h ( x ) c}{x})

Lösung

\frac{c ( x \frac{\partial}{\partial x} ( h ( x ) ) - h ( x ) )}{x ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{h ( x ) c}{x})

Entferne die Konstante:

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

= c \frac{\partial}{\partial x} (\frac{h ( x )}{x})

Wende die Quotientenregel an:

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

= c \frac{\frac{\partial}{\partial x} ( h ( x ) ) x - \frac{\partial}{\partial x} ( x ) h ( x )}{x ^{2}}

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

= c \frac{\frac{\partial}{\partial x} ( h ( x ) ) x - 1 \cdot h ( x )}{x ^{2}}

Vereinfache

c \frac{\frac{\partial}{\partial x} ( h ( x ) ) x - 1 \cdot h ( x )}{x ^{2}} : \frac{c ( x \frac{\partial}{\partial x} ( h ( x ) ) - h ( x ) )}{x ^{2}}

= \frac{c ( x \frac{\partial}{\partial x} ( h ( x ) ) - h ( x ) )}{x ^{2}}

Beliebte Beispiele

integral of 1/(4sqrt(x)(3+\sqrt{x))}

\int \frac{1}{4 x ( 3 + x )} d x

integral of (7sqrt(x))/(x-1)

\int \frac{7 x}{x - 1} d x

derivative sqrt(2x-x^2)

d er i v a t i v e 2 x - x^{2}

limit as x approaches infinity of (2x^3+3x-4)/(5-4x^3)

x \to \infty lim (\frac{2 x ^{3} + 3 x - 4}{5 - 4 x ^{3}})

f^{^{'}} (x) = x^{2} e^{x}