derivative of (1+csc(x^7)/(1-cot(x^7)))

解答

\frac{d}{d x} (\frac{1 + csc ( x ^{7} )}{1 - cot ( x ^{7} )})

\frac{- 7 x ^{6} cot ( x ^{7} ) csc ( x ^{7} ) ( 1 - cot ( x ^{7} ) ) - 7 x ^{6} csc ^{2} ( x ^{7} ) ( 1 + csc ( x ^{7} ) )}{( 1 - cot ( x ^{7} ) ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{1 + csc ( x ^{7} )}{1 - cot ( x ^{7} )})

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} ( 1 + csc ( x ^{7} ) ) ( 1 - cot ( x ^{7} ) ) - \frac{d}{d x} ( 1 - cot ( x ^{7} ) ) ( 1 + csc ( x ^{7} ) )}{( 1 - cot ( x ^{7} ) ) ^{2}}

\frac{d}{d x} (1 + csc (x^{7})) = - 7 x^{6} cot (x^{7}) csc (x^{7})

\frac{d}{d x} (1 - cot (x^{7})) = 7 x^{6} csc^{2} (x^{7})

= \frac{( - 7 x ^{6} cot ( x ^{7} ) csc ( x ^{7} ) ) ( 1 - cot ( x ^{7} ) ) - 7 x ^{6} csc ^{2} ( x ^{7} ) ( 1 + csc ( x ^{7} ) )}{( 1 - cot ( x ^{7} ) ) ^{2}}

化简

= \frac{- 7 x ^{6} cot ( x ^{7} ) csc ( x ^{7} ) ( 1 - cot ( x ^{7} ) ) - 7 x ^{6} csc ^{2} ( x ^{7} ) ( 1 + csc ( x ^{7} ) )}{( 1 - cot ( x ^{7} ) ) ^{2}}

d er i v a t i v e \frac{9}{x - 6}

\int_{1}^{5} 1 + (4)^{2} d x

\frac{d}{d x} (\frac{3}{2 x})

x \to 1 lim (- 3 a x + b)

\frac{d}{d x} ((13 x^{2} - 26 x + 26) e^{x})