derivative of (arccot(x)^5)

解答

\frac{d}{d x} ((arccot (x))^{5})

- \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

求解步骤

\frac{d}{d x} ((arccot (x))^{5})

使用连锁律:

5 (arccot (x))^{4} \frac{d}{d x} (arccot (x))

= 5 (arccot (x))^{4} \frac{d}{d x} (arccot (x))

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

= 5 (arccot (x))^{4} (- \frac{1}{x ^{2} + 1})

化简

5 arccot^{4} (x) (- \frac{1}{x ^{2} + 1}) : - \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

= - \frac{5 arccot ^{4} ( x )}{x ^{2} + 1}

\int \frac{- 1}{y ^{2} + 1} d y

y^{^{''}} + 2 y = sin (2 t), y (0) = 0, y^{^{'}} (0) = 0

\int \frac{1}{sec ( x ) + tan ( x )} d x

in v erse l a pl a ce \frac{1}{s ^{3} + 8 s ^{2} + 12 s}

d er i v a t i v e f (x) = 4 x^{\frac{4}{3}} - \frac{2}{3} x^{\frac{3}{2}} + x^{2} - 4 x + 1