derivative of cos^3(e^{-x})

Lösung

\frac{d}{d x} (cos^{3} (e^{- x}))

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

Schritte zur Lösung

\frac{d}{d x} (cos^{3} (e^{- x}))

Wende die Kettenregel an:

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

= 3 (cos (e^{- x}))^{2} \frac{d}{d x} (cos (e^{- x}))

\frac{d}{d x} (cos (e^{- x})) = e^{- x} sin (e^{- x})

= 3 (cos (e^{- x}))^{2} e^{- x} sin (e^{- x})

Vereinfache

= 3 e^{- x} cos^{2} (e^{- x}) sin (e^{- x})

\int cos (\frac{mπ x}{3}) d x

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y^{^{''}} + 2 y^{^{'}} + 2 y = sin (2 x)

x \to 0 + lim (e^{- \frac{5}{x}})

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