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Beliebt Rechnen >

derivative e^{-(t-3)^2}

Lösung

ableitung von

e^{- (t - 3)^{2}}

Lösung

e^{- t^{2} + 6 t - 9} (- 2 t + 6)

Schritte zur Lösung

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

Vereinfache

e^{- (t - 3)^{2}} : e^{- t^{2} + 6 t - 9}

= \frac{d}{d t} (e^{- t^{2} + 6 t - 9})

Wende die Kettenregel an:

e^{- t^{2} + 6 t - 9} \frac{d}{d t} (- t^{2} + 6 t - 9)

= e^{- t^{2} + 6 t - 9} \frac{d}{d t} (- t^{2} + 6 t - 9)

\frac{d}{d t} (- t^{2} + 6 t - 9) = - 2 t + 6

= e^{- t^{2} + 6 t - 9} (- 2 t + 6)

Graph

Beliebte Beispiele

(\partial)/(\partial y)(x^3y^4)

\frac{\partial}{\partial y} (x^{3} y^{4})

d/(dy)(cos(x^2)-y)

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

integral from-4 to 6 of 6

\int_{- 4}^{6} 6 d x

tangent f(x)=-4x^2-4x+4,\at x=1

t an g e n t f (x) = - 4 x^{2} - 4 x + 4, at x = 1

tangent-(12)/((4x+1)^2)

t an g e n t - \frac{12}{( 4 x + 1 ) ^{2}}