(\partial)/(\partial x)(3sec^2(3x-2y+1))

解答

\frac{\partial}{\partial x} (3 sec^{2} (3 x - 2 y + 1))

18 sec^{2} (3 x - 2 y + 1) tan (3 x - 2 y + 1)

求解步骤

\frac{\partial}{\partial x} (3 sec^{2} (3 x - 2 y + 1))

将

y

视为常数

将常数提出:

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

= 3 \frac{\partial}{\partial x} (sec^{2} (3 x - 2 y + 1))

使用连锁律:

2 sec (3 x - 2 y + 1) \frac{\partial}{\partial x} (sec (3 x - 2 y + 1))

= 2 sec (3 x - 2 y + 1) \frac{\partial}{\partial x} (sec (3 x - 2 y + 1))

\frac{\partial}{\partial x} (sec (3 x - 2 y + 1)) = sec (3 x - 2 y + 1) tan (3 x - 2 y + 1) \cdot 3

= 3 \cdot 2 sec (3 x - 2 y + 1) sec (3 x - 2 y + 1) tan (3 x - 2 y + 1) \cdot 3

化简

3 \cdot 2 sec (3 x - 2 y + 1) sec (3 x - 2 y + 1) tan (3 x - 2 y + 1) \cdot 3 : 18 sec^{2} (3 x - 2 y + 1) tan (3 x - 2 y + 1)

= 18 sec^{2} (3 x - 2 y + 1) tan (3 x - 2 y + 1)

\frac{d}{d x} ((2 x + 3)^{5} + 10 x (2 x + 3)^{4})

21 x y^{^{'}} + y = 462 x

\int_{0}^{\frac{π}{3}} ln (sec (x)) d x

\frac{d}{d x} (\frac{e ^{x}}{8 + e ^{x}})

\int - 14 x^{- 4} y^{6} + 16 x^{- 5} y^{7} d y