derivative of sqrt((x^2+1/(x^2+4)))

解答

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

\frac{3 x}{x ^{2} + 1 ( x ^{2} + 4 ) ^{\frac{3}{2}}}

求解步骤

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

使用连锁律:

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

= \frac{1}{2 \frac{x ^{2} + 1}{x ^{2} + 4}} \frac{d}{d x} (\frac{x ^{2} + 1}{x ^{2} + 4})

\frac{d}{d x} (\frac{x ^{2} + 1}{x ^{2} + 4}) = \frac{6 x}{( x ^{2} + 4 ) ^{2}}

= \frac{1}{2 \frac{x ^{2} + 1}{x ^{2} + 4}} \cdot \frac{6 x}{( x ^{2} + 4 ) ^{2}}

化简

\frac{1}{2 \frac{x ^{2} + 1}{x ^{2} + 4}} \cdot \frac{6 x}{( x ^{2} + 4 ) ^{2}} : \frac{3 x}{x ^{2} + 1 ( x ^{2} + 4 ) ^{\frac{3}{2}}}

= \frac{3 x}{x ^{2} + 1 ( x ^{2} + 4 ) ^{\frac{3}{2}}}

d er i v a t i v e 6 3 x

\frac{\partial}{\partial x} (2 x^{4} y + sin (x^{4}))

\int \frac{arcsin ( ln ( x ) )}{x} d x

d er i v a t i v e \frac{1}{cos ( \frac{x}{2} )}

\frac{d}{d x} (- \frac{2 ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{3}})