derivative f(x)=-tan(x)-5cot(x)

解答

导数

f (x) = - tan (x) - 5 cot (x)

- sec^{2} (x) + 5 csc^{2} (x)

求解步骤

\frac{d}{d x} (- tan (x) - 5 cot (x))

使用微分加减法定则:

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

= - \frac{d}{d x} (tan (x)) - \frac{d}{d x} (5 cot (x))

\frac{d}{d x} (tan (x)) = sec^{2} (x)

\frac{d}{d x} (5 cot (x)) = - 5 csc^{2} (x)

= - sec^{2} (x) - (- 5 csc^{2} (x))

化简

= - sec^{2} (x) + 5 csc^{2} (x)

\frac{d}{d x} (x (x - 1)^{3})

\int - x^{2} (x + 1)^{3} (x - 1) d x

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

\int_{0}^{3} (- x^{2} + x - 1) d x

\int_{1}^{16} \frac{1}{x} d x