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Beliebt Rechnen >

derivative of 3e^xsin(x)

Lösung

\frac{d}{d x} (3 e^{x} sin (x))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (3 e^{x} sin (x))

Entferne die Konstante:

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

= 3 \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)

= 3 (\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)

= 3 (e^{x} sin (x) + cos (x) e^{x})

Graph

Beliebte Beispiele

y^{''}+16y=-16sec^2(4x)

y^{^{''}} + 16 y = - 16 sec^{2} (4 x)

(\partial)/(\partial x)((c+1)/(c+x))

\frac{\partial}{\partial x} (\frac{c + 1}{c + x})

derivative of (x-3/(x+2))

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

(dy)/(dx)=3xsqrt(y)

\frac{d y}{d x} = 3 x y

f(x)=arccos(x^2)

f (x) = arccos (x^{2})