(\partial)/(\partial x)(x/(3+6x^2+7y^2))

Lösung

\frac{\partial}{\partial x} (\frac{x}{3 + 6 x ^{2} + 7 y ^{2}})

\frac{- 6 x ^{2} + 7 y ^{2} + 3}{( 3 + 6 x ^{2} + 7 y ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x}{3 + 6 x ^{2} + 7 y ^{2}})

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 ) ( 3 + 6 x ^{2} + 7 y ^{2} ) - \frac{\partial}{\partial x} ( 3 + 6 x ^{2} + 7 y ^{2} ) x}{( 3 + 6 x ^{2} + 7 y ^{2} ) ^{2}}

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

\frac{\partial}{\partial x} (3 + 6 x^{2} + 7 y^{2}) = 12 x

= \frac{1 \cdot ( 3 + 6 x ^{2} + 7 y ^{2} ) - 12 xx}{( 3 + 6 x ^{2} + 7 y ^{2} ) ^{2}}

1 \cdot (3 + 6 x^{2} + 7 y^{2}) - 12 xx = - 6 x^{2} + 7 y^{2} + 3

= \frac{- 6 x ^{2} + 7 y ^{2} + 3}{( 3 + 6 x ^{2} + 7 y ^{2} ) ^{2}}

\frac{d}{d x} (arcsin (x y))

f (x) = \frac{x e ^{x}}{x + e ^{x}}

\int \frac{4}{( x + 2 ) ( x - 2 )} d x

\int_{0}^{1} \frac{x - 1}{x ^{2} + 3 x + 2} d x

t an g e n t f (x) = \frac{e ^{x}}{x}, at x = 1