derivative of (x^2+6/((2x-7)^7))

解答

\frac{d}{d x} (\frac{x ^{2} + 6}{( 2 x - 7 ) ^{7}})

\frac{2 ( - 5 x ^{2} - 7 x - 42 )}{( 2 x - 7 ) ^{8}}

求解步骤

\frac{d}{d x} (\frac{x ^{2} + 6}{( 2 x - 7 ) ^{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} ( x ^{2} + 6 ) ( 2 x - 7 ) ^{7} - \frac{d}{d x} ( ( 2 x - 7 ) ^{7} ) ( x ^{2} + 6 )}{( ( 2 x - 7 ) ^{7} ) ^{2}}

\frac{d}{d x} (x^{2} + 6) = 2 x

\frac{d}{d x} ((2 x - 7)^{7}) = 14 (2 x - 7)^{6}

= \frac{2 x ( 2 x - 7 ) ^{7} - 14 ( 2 x - 7 ) ^{6} ( x ^{2} + 6 )}{( ( 2 x - 7 ) ^{7} ) ^{2}}

化简

\frac{2 x ( 2 x - 7 ) ^{7} - 14 ( 2 x - 7 ) ^{6} ( x ^{2} + 6 )}{( ( 2 x - 7 ) ^{7} ) ^{2}} : \frac{2 ( - 5 x ^{2} - 7 x - 42 )}{( 2 x - 7 ) ^{8}}

= \frac{2 ( - 5 x ^{2} - 7 x - 42 )}{( 2 x - 7 ) ^{8}}

x \to 0 lim (\frac{200 π}{x})

n or ma l y = \frac{y + 5 x}{3 y - x}, (1, 2)

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

d er i v a t i v e 1 + t

\int (2 x + 3) e^{2 x} d x