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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- x}, g = cos (x)

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

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

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

= (- e^{- x}) cos (x) + (- sin (x)) e^{- x}

Vereinfache

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

Graph

Beliebte Beispiele

inverselaplace 1/(s^2+s+2)

in v erse l a pl a ce \frac{1}{s ^{2} + s + 2}

sum from n=0 to infinity of ((7-8n))/(4+3n)

n = 0 \sum \infty \frac{( 7 - 8 n )}{4 + 3 n}

integral of-6/(x^2)

\int - \frac{6}{x ^{2}} d x

tangent sqrt(5x+1),\at x=7

t an g e n t 5 x + 1, at x = 7

derivative of (x/(x+1)^x)

\frac{d}{d x} ((\frac{x}{x + 1})^{x})