derivative of (sqrt(x)/(sqrt(x+1)))

解答

\frac{d}{d x} (\frac{x}{x + 1})

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

求解步骤

\frac{d}{d x} (\frac{x}{x + 1})

化简

\frac{x}{x + 1} : \frac{x}{x + 1}

= \frac{d}{d x} (\frac{x}{x + 1})

使用连锁律:

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

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

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

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

化简

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

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

t an g e n t f (x) = 8 x (x + 2), at x = 3

d er i v a t i v e t^{3} - \frac{1}{4 t ^{5}}

\int cot^{3} (x) csc^{5} (x) d x

\int sin (2 x) cos^{5} (2 x) d x

\frac{\partial}{\partial x} (x^{4} sin (y^{9} z^{9}))