derivative of e^{2x}cos(x)

Lösung

\frac{d}{d x} (e^{2 x} cos (x))

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

Schritte zur Lösung

\frac{d}{d x} (e^{2 x} cos (x))

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

d er i v a t i v e y = sin^{5} (x)

n = 0 \sum \infty 2^{(3 - 2 n)}

a re a x = 1 - y^{2}, x = y^{2} - 1

d er i v a t i v e \frac{( - 2 x - 3 ) ^{7}}{( 4 x + 2 ) ^{4}}