(\partial)/(\partial x)(x/(x^7-y^6))

Lösung

\frac{\partial}{\partial x} (\frac{x}{x ^{7} - y ^{6}})

\frac{- 6 x ^{7} - y ^{6}}{( x ^{7} - y ^{6} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x}{x ^{7} - y ^{6}})

Behandle

y

als Konstante

Wende die Quotientenregel an:

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

= \frac{\frac{\partial}{\partial x} ( x ) ( x ^{7} - y ^{6} ) - \frac{\partial}{\partial x} ( x ^{7} - y ^{6} ) x}{( x ^{7} - y ^{6} ) ^{2}}

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

\frac{\partial}{\partial x} (x^{7} - y^{6}) = 7 x^{6}

= \frac{1 \cdot ( x ^{7} - y ^{6} ) - 7 x ^{6} x}{( x ^{7} - y ^{6} ) ^{2}}

1 \cdot (x^{7} - y^{6}) - 7 x^{6} x = - 6 x^{7} - y^{6}

= \frac{- 6 x ^{7} - y ^{6}}{( x ^{7} - y ^{6} ) ^{2}}

\int (x^{2} - 5)^{5} (2 x) d x

\frac{d}{d x} (\frac{5}{( 4 x ) ^{- 2}})

\frac{d}{d x} (cos (wt))

\int_{0}^{\frac{π}{20}} tan (10 x) d x

d er i v a t i v e f (x) = (2 x - 3) \cdot x