derivative of 1/((3^{(-x^2-y^2)+1)})

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

y^{^{''}} - 0.2 y^{^{'}} + 0.01 y = 0, y (0) = 13, y^{^{'}} (0) = b

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

\int \frac{1}{u ^{2} + 3} d u

\frac{d x}{d y} = \frac{y ^{3} - 3 x}{y}

n = 1 \sum \infty \frac{4}{2 n}