derivative (s^6+1/s)^{5/2}

解答

导数

(s^{6} + \frac{1}{s})^{\frac{5}{2}}

\frac{5 ( s ^{6} + \frac{1}{s} ) ^{\frac{3}{2}}}{2} (6 s^{5} - \frac{1}{s ^{2}})

求解步骤

\frac{d}{d s} ((s^{6} + \frac{1}{s})^{\frac{5}{2}})

使用连锁律:

\frac{5 ( s ^{6} + \frac{1}{s} ) ^{\frac{3}{2}}}{2} \frac{d}{d s} (s^{6} + \frac{1}{s})

= \frac{5 ( s ^{6} + \frac{1}{s} ) ^{\frac{3}{2}}}{2} \frac{d}{d s} (s^{6} + \frac{1}{s})

\frac{d}{d s} (s^{6} + \frac{1}{s}) = 6 s^{5} - \frac{1}{s ^{2}}

= \frac{5 ( s ^{6} + \frac{1}{s} ) ^{\frac{3}{2}}}{2} (6 s^{5} - \frac{1}{s ^{2}})

\frac{\partial}{\partial y} (3 x^{2} + 8 x y + y^{2})

\int \frac{2 x + 3}{2 x + 4} d x

d er i v a t i v e p (x) = x^{3} - 5 x^{2} - 4 x + 20

d er i v a t i v e 8 + cos (t^{2})

x \to \frac{3 π}{2} lim (- 2 tan (x))