(\partial)/(\partial x)((3x^5-7)/(4x))

Lösung

\frac{\partial}{\partial x} (\frac{3 x ^{5} - 7}{4 x})

\frac{12 x ^{5} + 7}{4 x ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{3 x ^{5} - 7}{4 x})

Entferne die Konstante:

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

= \frac{1}{4} \frac{\partial}{\partial x} (\frac{3 x ^{5} - 7}{x})

Wende die Quotientenregel an:

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

= \frac{1}{4} \cdot \frac{\frac{\partial}{\partial x} ( 3 x ^{5} - 7 ) x - \frac{\partial}{\partial x} ( x ) ( 3 x ^{5} - 7 )}{x ^{2}}

\frac{\partial}{\partial x} (3 x^{5} - 7) = 15 x^{4}

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

= \frac{1}{4} \cdot \frac{15 x ^{4} x - 1 \cdot ( 3 x ^{5} - 7 )}{x ^{2}}

Vereinfache

\frac{1}{4} \cdot \frac{15 x ^{4} x - 1 \cdot ( 3 x ^{5} - 7 )}{x ^{2}} : \frac{12 x ^{5} + 7}{4 x ^{2}}

= \frac{12 x ^{5} + 7}{4 x ^{2}}

x \to 8 lim (\frac{1}{( x - 8 ) ^{2}})

csc (y) d x + sec (x) d y = 0

\frac{d}{d x} (10 - x^{2})

s l o p e y = x^{3} - 9 x

\frac{d y}{d x} = - 9 y