derivative of (e^{2x}/(1+sin(pix)))

Lösung

\frac{d}{d x} (\frac{e ^{2 x}}{1 + sin ( π x )})

\frac{e ^{2 x} \cdot 2 ( 1 + sin ( π x ) ) - π cos ( π x ) e ^{2 x}}{( 1 + sin ( π x ) ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{2 x}}{1 + sin ( π x )})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{2 x} ) ( 1 + sin ( π x ) ) - \frac{d}{d x} ( 1 + sin ( π x ) ) e ^{2 x}}{( 1 + sin ( π x ) ) ^{2}}

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

\frac{d}{d x} (1 + sin (π x)) = π cos (π x)

= \frac{e ^{2 x} \cdot 2 ( 1 + sin ( π x ) ) - π cos ( π x ) e ^{2 x}}{( 1 + sin ( π x ) ) ^{2}}

x \to 3 - lim (- \frac{1}{x - 3})

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

y^{^{''}} + 3 y^{^{'}} = 6 e^{- 3 t}, y (0) = 8, y^{^{'}} (0) = - 4

\frac{d}{d x} (e^{x} x^{3} + 6 e^{x} x^{2} + 6 e^{x} x)

y^{2} d x - (1 - x) d y = 0