derivative of (3csc(x)/(4^x))

解答

\frac{d}{d x} (\frac{3 csc ( x )}{4 ^{x}})

\frac{3 ( - 4 ^{x} cot ( x ) csc ( x ) - ln ( 2 ) \cdot 2 ^{2 x + 1} csc ( x ) )}{1 6 ^{x}}

求解步骤

\frac{d}{d x} (\frac{3 csc ( x )}{4 ^{x}})

将常数提出:

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

= 3 \frac{d}{d x} (\frac{csc ( x )}{4 ^{x}})

使用微分除法定则:

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

= 3 \cdot \frac{\frac{d}{d x} ( csc ( x ) ) 4 ^{x} - \frac{d}{d x} ( 4 ^{x} ) csc ( x )}{( 4 ^{x} ) ^{2}}

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

\frac{d}{d x} (4^{x}) = ln (2) \cdot 2^{2 x + 1}

= 3 \cdot \frac{( - cot ( x ) csc ( x ) ) \cdot 4 ^{x} - ln ( 2 ) \cdot 2 ^{2 x + 1} csc ( x )}{( 4 ^{x} ) ^{2}}

化简

3 \cdot \frac{( - cot ( x ) csc ( x ) ) \cdot 4 ^{x} - ln ( 2 ) \cdot 2 ^{2 x + 1} csc ( x )}{( 4 ^{x} ) ^{2}} : \frac{3 ( - 4 ^{x} cot ( x ) csc ( x ) - ln ( 2 ) \cdot 2 ^{2 x + 1} csc ( x ) )}{1 6 ^{x}}

= \frac{3 ( - 4 ^{x} cot ( x ) csc ( x ) - ln ( 2 ) \cdot 2 ^{2 x + 1} csc ( x ) )}{1 6 ^{x}}

\int \frac{5}{2} x d x

\frac{\partial}{\partial x} (sec (17 x))

\frac{\partial}{\partial x} (25 - (x^{2} + 3 y^{2}))

\int 2 y + z d x

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = 2 sin (x)