derivative of (cos(6x)/(e^x))

解答

\frac{d}{d x} (\frac{cos ( 6 x )}{e ^{x}})

- \frac{6 sin ( 6 x ) + cos ( 6 x )}{e ^{x}}

求解步骤

\frac{d}{d x} (\frac{cos ( 6 x )}{e ^{x}})

使用微分除法定则:

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

= \frac{\frac{d}{d x} ( cos ( 6 x ) ) e ^{x} - \frac{d}{d x} ( e ^{x} ) cos ( 6 x )}{( e ^{x} ) ^{2}}

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

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

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

化简

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

= - \frac{6 sin ( 6 x ) + cos ( 6 x )}{e ^{x}}

d er i v a t i v e y = arctan (x)

x^{2} y^{^{'}} = 2 x^{2} + x y + 2 y^{2}

\int \frac{( 5 - 4 x ^{2} )}{( 3 + 2 x )} d x

\frac{\partial}{\partial x} (x y + x + y)

(y^{- 1})^{^{'}}