derivative cot(sqrt(x^2+pix))

解答

导数

cot (x^{2} + π x)

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

求解步骤

\frac{d}{d x} (cot (x^{2} + π x))

使用连锁律:

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

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

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

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

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

in v erse l a pl a ce \frac{s + 1}{( s ^{2} + 2 ) ( s + 1 )}

d er i v a t i v e 9 sin (2 x)

t an g e n t f (x) = \frac{x}{4 + x ^{2}}

(4^{x})^{^{'}}

n = 1 \sum \infty ln (\frac{n}{n + 1})