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Beliebt Rechnen >

(\partial)/(\partial x)(1/(x+4y))

Lösung

\frac{\partial}{\partial x} (\frac{1}{x + 4 y})

Lösung

- \frac{1}{( x + 4 y ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{x + 4 y})

Behandle

y

als Konstante

Wende Exponentenregel an:

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

= \frac{\partial}{\partial x} ((x + 4 y)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( x + 4 y ) ^{2}} \frac{\partial}{\partial x} (x + 4 y)

= - \frac{1}{( x + 4 y ) ^{2}} \frac{\partial}{\partial x} (x + 4 y)

\frac{\partial}{\partial x} (x + 4 y) = 1

= - \frac{1}{( x + 4 y ) ^{2}} \cdot 1

Vereinfache

= - \frac{1}{( x + 4 y ) ^{2}}

Beliebte Beispiele

integral of 28t(7t^2-5)^3

\int 28 t (7 t^{2} - 5)^{3} d t

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

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

integral of (x^2)/((16+x^2)^2)

\int \frac{x ^{2}}{( 16 + x ^{2} ) ^{2}} d x

integral of (8x-7)*ln(x)

\int (8 x - 7) \cdot ln (x) d x

fläche xsqrt(8-2x^2),0,2

a re a x 8 - 2 x^{2}, 0, 2