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Beliebt Rechnen >

derivative e^{ax}sin(bx)

Lösung

ableitung von

e^{a x} sin (b x)

Lösung

e^{a x} a sin (b x) + cos (b x) b e^{a x}

Schritte zur Lösung

\frac{d}{d x} (e^{a x} sin (b x))

Wende die Produktregel an:

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

f = e^{a x}, g = sin (b x)

= \frac{d}{d x} (e^{a x}) sin (b x) + \frac{d}{d x} (sin (b x)) e^{a x}

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

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

= e^{a x} a sin (b x) + cos (b x) b e^{a x}

Graph

Beliebte Beispiele

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

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

integral of e^{-x}cos^2(x)

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

integral of (xsqrt(9-x^2))

\int (x 9 - x^{2}) d x

(dy)/(dx)=e^{2y+2x}

\frac{d y}{d x} = e^{2 y + 2 x}

derivative of x-3x^2

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