derivative of i/(sqrt(5x^2+1))

解答

\frac{d}{d x} (\frac{i}{5 x ^{2} + 1})

- \frac{5 i x}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}}

求解步骤

\frac{d}{d x} (\frac{i}{5 x ^{2} + 1})

化简

\frac{i}{5 x ^{2} + 1} : i \frac{1 + 5 x ^{2}}{1 + 5 x ^{2}}

= \frac{d}{d x} (i \frac{1 + 5 x ^{2}}{1 + 5 x ^{2}})

将常数提出:

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

= i \frac{d}{d x} (\frac{1 + 5 x ^{2}}{1 + 5 x ^{2}})

使用微分除法定则:

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

= i \frac{\frac{d}{d x} ( 1 + 5 x ^{2} ) ( 1 + 5 x ^{2} ) - \frac{d}{d x} ( 1 + 5 x ^{2} ) 1 + 5 x ^{2}}{( 1 + 5 x ^{2} ) ^{2}}

\frac{d}{d x} (1 + 5 x^{2}) = \frac{5 x}{1 + 5 x ^{2}}

\frac{d}{d x} (1 + 5 x^{2}) = 10 x

= i \frac{\frac{5 x}{1 + 5 x ^{2}} ( 1 + 5 x ^{2} ) - 10 x 1 + 5 x ^{2}}{( 1 + 5 x ^{2} ) ^{2}}

化简

i \frac{\frac{5 x}{1 + 5 x ^{2}} ( 1 + 5 x ^{2} ) - 10 x 1 + 5 x ^{2}}{( 1 + 5 x ^{2} ) ^{2}} : - \frac{5 i x}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}}

= - \frac{5 i x}{( 1 + 5 x ^{2} ) ^{\frac{3}{2}}}

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

\int ln (4 - x) d x

\frac{d f ^{- 1}}{d x} f (x) = 3 x^{3} - 5 x^{2} - 2, x = 1272

d er i v a t i v e \frac{1 + x}{1 + e ^{x}}

a re a x = 8 y^{2}, x = 20 + 3 y^{2}