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Beliebt Rechnen >

derivative of 5e^xsin(x)

Lösung

\frac{d}{d x} (5 e^{x} sin (x))

Lösung

5 (e^{x} sin (x) + cos (x) e^{x})

Schritte zur Lösung

\frac{d}{d x} (5 e^{x} sin (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (e^{x} sin (x))

Wende die Produktregel an:

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

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

= 5 (\frac{d}{d x} (e^{x}) sin (x) + \frac{d}{d x} (sin (x)) e^{x})

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

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

= 5 (e^{x} sin (x) + cos (x) e^{x})

Graph

Beliebte Beispiele

derivative s(t)=t^3-5t^2-3t+8

d er i v a t i v e s (t) = t^{3} - 5 t^{2} - 3 t + 8

(dy)/(dx)+y/x =2x^6y^2

\frac{d y}{d x} + \frac{y}{x} = 2 x^{6} y^{2}

derivative f(x)=x^2*e^{-x^2}

d er i v a t i v e f (x) = x^{2} \cdot e^{- x^{2}}

f (x) = \frac{50}{x}

integral of y^{4/3}

\int y^{\frac{4}{3}} d y