(\partial)/(\partial y)(ytsec^2(yt))

解答

\frac{\partial}{\partial y} (y t sec^{2} (y t))

t (sec^{2} (y t) + 2 y t sec^{2} (y t) tan (y t))

求解步骤

\frac{\partial}{\partial y} (y t sec^{2} (y t))

将

t

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= t \frac{\partial}{\partial y} (y sec^{2} (y t))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = sec^{2} (y t)

= t (\frac{\partial}{\partial y} (y) sec^{2} (y t) + \frac{\partial}{\partial y} (sec^{2} (y t)) y)

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (sec^{2} (y t)) = 2 t sec^{2} (t y) tan (t y)

= t (1 \cdot sec^{2} (y t) + 2 t sec^{2} (t y) tan (t y) y)

化简

= t (sec^{2} (y t) + 2 y t sec^{2} (y t) tan (y t))

t an g e n t \frac{x - 3}{9 x - 2}

(3 + 2 x^{- 1} y + 2 x^{- 1} y^{2}) d x + (1 + 2 y) d y = 0

t an g e n t \frac{6 x}{x + 8}, at x = 1

\int (5 sec^{2} (x)) d x

x \to 6 - lim (c x^{2} + 5 x)