d/(dA)((1+cot(A))/(csc(A)))

解答

\frac{d}{d A} (\frac{1 + cot ( A )}{csc ( A )})

- sin (A) + cos (A)

求解步骤

\frac{d}{d A} (\frac{1 + cot ( A )}{csc ( A )})

化简

\frac{1 + cot ( A )}{csc ( A )} : cos (A) + sin (A)

= \frac{d}{d A} (cos (A) + sin (A))

使用微分加减法定则:

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

= \frac{d}{d A} (cos (A)) + \frac{d}{d A} (sin (A))

\frac{d}{d A} (cos (A)) = - sin (A)

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

= - sin (A) + cos (A)

t an g e n t f (x) = x^{4} - 3 x^{2} + 5, at x = - 1

\frac{d y}{d x} - y = x^{2} sin (x)

\frac{d}{d t} (t - sin (t))

\frac{\partial}{\partial y} (sin (x + y) + (x + y))

x^{2} y \frac{d y}{d x} = e^{x}