derivative of (2x-x^2/(sqrt(x))-3cot(x))

解答

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

\frac{2 - 3 x}{2 x} + 3 csc^{2} (x)

求解步骤

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

化简

\frac{2 x - x ^{2}}{x} - 3 cot (x) : x (2 - x) - 3 cot (x)

= \frac{d}{d x} (x (2 - x) - 3 cot (x))

使用微分加减法定则:

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

= \frac{d}{d x} (x (2 - x)) - \frac{d}{d x} (3 cot (x))

\frac{d}{d x} (x (2 - x)) = \frac{2 - 3 x}{2 x}

\frac{d}{d x} (3 cot (x)) = - 3 csc^{2} (x)

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

化简

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

x \to 4 lim (2 x^{2} + 7)

\frac{d h}{d t} = \frac{( 7 - e ^{- \frac{t}{5}} )}{6} - \frac{2}{9} h

s l o p e 2 x y^{3} = x y + 6

\int \frac{1}{4 x} + 9 d x

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