derivative of (5x+2/(3x-4))

解答

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

- \frac{26}{( 3 x - 4 ) ^{2}}

求解步骤

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

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

\frac{d}{d x} (5 x + 2) = 5

\frac{d}{d x} (3 x - 4) = 3

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

化简

\frac{5 ( 3 x - 4 ) - 3 ( 5 x + 2 )}{( 3 x - 4 ) ^{2}} : - \frac{26}{( 3 x - 4 ) ^{2}}

= - \frac{26}{( 3 x - 4 ) ^{2}}

in v erse l a pl a ce \frac{1}{( s - 1 ) ^{2} ( s + 5 )}

t an g e n t f (x) = sin (sin (x)), at x = 4 π

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

d er i v a t i v e y = e^{4 x^{2}} + 1

t an g e n t f (x) = tan (x), at x = 1