(\partial)/(\partial x)(-x/((x^2+y^2)))

Lösung

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

- \frac{- x ^{2} + y ^{2}}{( x ^{2} + y ^{2} ) ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

\frac{\partial}{\partial x} (x^{2} + y^{2}) = 2 x

= - \frac{1 \cdot ( x ^{2} + y ^{2} ) - 2 xx}{( x ^{2} + y ^{2} ) ^{2}}

1 \cdot (x^{2} + y^{2}) - 2 xx = - x^{2} + y^{2}

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

y^{^{''}} - 2 y^{^{'}} + y = 8 e^{x}

x \to 0 + lim ((ln (x))^{2})

d er i v a t i v e sec^{2} (x) + tan^{2} (x)

t an g e n t f (x) = 15 x - 1.86 x^{2}, at x = a

\frac{d}{d x} (7^{x^{2}})