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Beliebt Rechnen >

derivative of e^xsin(xcos(x))

Lösung

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

Lösung

e^{x} sin (x) cos (x) + cos (2 x) e^{x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (sin (x) cos (x)) = cos (2 x)

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

Graph

Beliebte Beispiele

fläche 7cos(7x),7-7cos(7x),[0, pi/7 ]

a re a 7 cos (7 x), 7 - 7 cos (7 x), [0, \frac{π}{7}]

derivative of 1/((3x+1^2))

\frac{d}{d x} (\frac{1}{( 3 x + 1 ) ^{2}})

f^'(x)=(3x^5-2)^{20}

f^{^{'}} (x) = (3 x^{5} - 2)^{20}

integral of 1/(x^{4/3)}

\int \frac{1}{x ^{\frac{4}{3}}} d x

integral from 1 to R of (ln(4x))/(x^2)

\int_{1}^{R} \frac{ln ( 4 x )}{x ^{2}} d x