derivative sin(x)+4/3 cot(x)

解答

导数

sin (x) + \frac{4}{3} cot (x)

cos (x) - \frac{4}{3} csc^{2} (x)

求解步骤

\frac{d}{d x} (sin (x) + \frac{4}{3} cot (x))

使用微分加减法定则:

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

= \frac{d}{d x} (sin (x)) + \frac{d}{d x} (\frac{4}{3} cot (x))

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (\frac{4}{3} cot (x)) = - \frac{4}{3} csc^{2} (x)

= cos (x) - \frac{4}{3} csc^{2} (x)

\int \frac{1}{x ^{2} - 7 x + 12} d x

x y^{2} \frac{d y}{d x} = y^{3} - 3 x^{3}, y (1) = 5

y^{^{'}} = 0.1 \cdot y - 250000

\int 5 cos (π x - 3) d x

d er i v a t i v e \frac{4 x}{x ^{2} + 2}