derivative of 10+((50x/(2x^2+9)))

解答

\frac{d}{d x} (10 + (\frac{50 x}{2 x ^{2} + 9}))

\frac{50 ( - 2 x ^{2} + 9 )}{( 2 x ^{2} + 9 ) ^{2}}

求解步骤

\frac{d}{d x} (10 + (\frac{50 x}{2 x ^{2} + 9}))

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (10) + \frac{d}{d x} (\frac{50 x}{2 x ^{2} + 9})

\frac{d}{d x} (10) = 0

\frac{d}{d x} (\frac{50 x}{2 x ^{2} + 9}) = \frac{50 ( - 2 x ^{2} + 9 )}{( 2 x ^{2} + 9 ) ^{2}}

= 0 + \frac{50 ( - 2 x ^{2} + 9 )}{( 2 x ^{2} + 9 ) ^{2}}

化简

= \frac{50 ( - 2 x ^{2} + 9 )}{( 2 x ^{2} + 9 ) ^{2}}

x \to 0 - lim (\frac{6}{x} - \frac{6}{∣ x ∣})

x \cdot y^{^{'}} + y = x^{4} \cdot y^{3}

\int t^{19} e^{- t^{20}} d t

in v erse l a pl a ce \frac{5}{s ^{3} - 2 s ^{2} - 3 s}

s l o p e in t erce pt (2005, 56), (2010, 59)