derivative f(x)=csc(sqrt(x+5))

解答

导数

f (x) = csc (x + 5)

- \frac{cot ( x + 5 ) csc ( x + 5 )}{2 x + 5}

求解步骤

\frac{d}{d x} (csc (x + 5))

使用连锁律:

- cot (x + 5) csc (x + 5) \frac{d}{d x} (x + 5)

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

\frac{d}{d x} (x + 5) = \frac{1}{2 x + 5}

= - cot (x + 5) csc (x + 5) \frac{1}{2 x + 5}

化简

- cot (x + 5) csc (x + 5) \frac{1}{2 x + 5} : - \frac{cot ( x + 5 ) csc ( x + 5 )}{2 x + 5}

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

f (x) = \frac{1}{3 x + 1}

y^{^{'}} = t e^{- y}, y (0) = 1

\int_{0}^{1} cos (2 π x) d x

x \to 3 lim (x - 1)

y^{^{''}} + 36 y = - 48 sin (6 t)