(\partial)/(\partial x)(1/(x^2+3y))

Lösung

\frac{\partial}{\partial x} (\frac{1}{x ^{2} + 3 y})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{x ^{2} + 3 y})

Behandle

y

als Konstante

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= \frac{\partial}{\partial x} ((x^{2} + 3 y)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( x ^{2} + 3 y ) ^{2}} \frac{\partial}{\partial x} (x^{2} + 3 y)

= - \frac{1}{( x ^{2} + 3 y ) ^{2}} \frac{\partial}{\partial x} (x^{2} + 3 y)

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

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

Vereinfache

- \frac{1}{( x ^{2} + 3 y ) ^{2}} \cdot 2 x : - \frac{2 x}{( x ^{2} + 3 y ) ^{2}}

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

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

y^{^{'}} + \frac{1 - x}{2 x} y = 0

d er i v a t i v e f (x) = 2 x + \frac{1936}{x}

t an g e n t f (x) = 110 x - 16 x^{2}, at x = 4

d er i v a t i v e \frac{1}{x + 8}