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

Lösung

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

\frac{- 5 x ^{6} - y ^{7}}{( x ^{6} - y ^{7} ) ^{2}}

Schritte zur Lösung

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

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

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

\frac{\partial}{\partial x} (x^{6} - y^{7}) = 6 x^{5}

= \frac{1 \cdot ( x ^{6} - y ^{7} ) - 6 x ^{5} x}{( x ^{6} - y ^{7} ) ^{2}}

1 \cdot (x^{6} - y^{7}) - 6 x^{5} x = - 5 x^{6} - y^{7}

= \frac{- 5 x ^{6} - y ^{7}}{( x ^{6} - y ^{7} ) ^{2}}

n = 4 \sum \infty (x + 1)^{n}

d er i v a t i v e f (x) = x^{- 8}

y^{^{'}} = - 2 y + t, y (0) = - 5

\int \frac{1}{y ^{2} - 3 y + 2} d y

\int (x^{2} + 3 x + 1) d x