derivative cos^2(e^x+sqrt(x))

解答

导数

cos^{2} (e^{x} + x)

- sin (2 (x + e^{x})) (\frac{1}{2 x} + e^{x})

求解步骤

\frac{d}{d x} (cos^{2} (e^{x} + x))

使用连锁律:

2 cos (e^{x} + x) \frac{d}{d x} (cos (e^{x} + x))

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

\frac{d}{d x} (cos (e^{x} + x)) = - sin (e^{x} + x) (e^{x} + \frac{1}{2 x})

= 2 cos (e^{x} + x) (- sin (e^{x} + x) (e^{x} + \frac{1}{2 x}))

化简

2 cos (e^{x} + x) (- sin (e^{x} + x) (e^{x} + \frac{1}{2 x})) : - sin (2 (x + e^{x})) (\frac{1}{2 x} + e^{x})

= - sin (2 (x + e^{x})) (\frac{1}{2 x} + e^{x})

\frac{\partial}{\partial y} (- e^{x - y} x)

\int x cos (8 x^{2} + π) d x

\int - 9 cos (3 x + π) d x

\frac{\partial}{\partial s} (\frac{t ^{2}}{s ^{3}})

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