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Beliebt Rechnen >

(\partial)/(\partial x)(cos(e^{-x^2}))

Lösung

\frac{\partial}{\partial x} (cos (e^{- x^{2}}))

Lösung

2 e^{- x^{2}} x sin (e^{- x^{2}})

Schritte zur Lösung

\frac{\partial}{\partial x} (cos (e^{- x^{2}}))

Wende die Kettenregel an:

- sin (e^{- x^{2}}) \frac{\partial}{\partial x} (e^{- x^{2}})

= - sin (e^{- x^{2}}) \frac{\partial}{\partial x} (e^{- x^{2}})

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

= - sin (e^{- x^{2}}) (- 2 e^{- x^{2}} x)

Vereinfache

= 2 e^{- x^{2}} x sin (e^{- x^{2}})

Beliebte Beispiele

derivative of x^{10}-1

\frac{d}{d x} (x^{10} - 1)

derivative of 4x^2-x^3

\frac{d}{d x} (4 x^{2} - x^{3})

integral of 6x^{-3}

\int 6 x^{- 3} d x

integral of (x^2+1)x

\int (x^{2} + 1) x d x

derivative y=(2x^3+7)^2

d er i v a t i v e y = (2 x^{3} + 7)^{2}