derivative of (e^x/(x*cos(x)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Wende Exponentenregel an:

(a \cdot b)^{n} = a^{n} b^{n}

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

f^{^{''}} + 16 f = sin (2 x)

\int_{6}^{12} 144 - x^{2} d x

x^{2} y^{^{''}} - 6 y = 0, y (1) = 6, y^{^{'}} (1) = - 2

\frac{\partial}{\partial x} (e^{x y} y^{2} + \frac{x}{y})

\int e^{- \frac{x ^{2}}{2}} d x