derivative of (3sqrt(x)-3sin(x)/(-e^x))

解答

\frac{d}{d x} (\frac{3 x - 3 sin ( x )}{- e ^{x}})

- \frac{3 - 6 x cos ( x ) - 6 x ( - sin ( x ) + x )}{2 e ^{x} x}

求解步骤

\frac{d}{d x} (\frac{3 x - 3 sin ( x )}{- e ^{x}})

化简

\frac{3 x - 3 sin ( x )}{- e ^{x}} : - \frac{3 x - 3 sin ( x )}{e ^{x}}

= \frac{d}{d x} (- \frac{3 x - 3 sin ( x )}{e ^{x}})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (\frac{3 x - 3 sin ( 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} ( 3 x - 3 sin ( x ) ) e ^{x} - \frac{d}{d x} ( e ^{x} ) ( 3 x - 3 sin ( x ) )}{( e ^{x} ) ^{2}}

\frac{d}{d x} (3 x - 3 sin (x)) = \frac{3}{2 x} - 3 cos (x)

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

= - \frac{( \frac{3}{2 x} - 3 cos ( x ) ) e ^{x} - e ^{x} ( 3 x - 3 sin ( x ) )}{( e ^{x} ) ^{2}}

化简

- \frac{( \frac{3}{2 x} - 3 cos ( x ) ) e ^{x} - e ^{x} ( 3 x - 3 sin ( x ) )}{( e ^{x} ) ^{2}} : - \frac{3 - 6 x cos ( x ) - 6 x ( - sin ( x ) + x )}{2 e ^{x} x}

= - \frac{3 - 6 x cos ( x ) - 6 x ( - sin ( x ) + x )}{2 e ^{x} x}

\int (1 + x^{3})^{- 1} d x

y^{^{''}} + y^{^{'}} - 2 y = 3 t

\frac{d}{d x} (e^{c o s (x^{2})})

\frac{d}{d x} (tan (e^{2 x}) + e^{t a n (2 x)})

x \to - 1 - lim (\frac{1}{( x + 1 ) ^{2}})