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Beliebt Rechnen >

derivative of e^{2x}sin(6x)

Lösung

\frac{d}{d x} (e^{2 x} sin (6 x))

Lösung

e^{2 x} \cdot 2 sin (6 x) + cos (6 x) \cdot 6 e^{2 x}

Schritte zur Lösung

\frac{d}{d x} (e^{2 x} sin (6 x))

Wende die Produktregel an:

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

f = e^{2 x}, g = sin (6 x)

= \frac{d}{d x} (e^{2 x}) sin (6 x) + \frac{d}{d x} (sin (6 x)) e^{2 x}

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (sin (6 x)) = cos (6 x) \cdot 6

= e^{2 x} \cdot 2 sin (6 x) + cos (6 x) \cdot 6 e^{2 x}

Graph

Beliebte Beispiele

derivative of (4x-12/((x-2)^2))

\frac{d}{d x} (\frac{4 x - 12}{( x - 2 ) ^{2}})

limit as x approaches 3-of sqrt(3-x)

x \to 3 - lim (3 - x)

integral of x^7sqrt(x^4+3)

\int x^{7} x^{4} + 3 d x

tangent f(x)= 3/(x+1),(2,1)

t an g e n t f (x) = \frac{3}{x + 1}, (2, 1)

y^{^{'}} = e^{- 3 x} + 2 x