(\partial)/(\partial x)(x^3sec^2(xy))

解答

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

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

求解步骤

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

将

y

视为常数

使用微分乘法定则:

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

f = x^{3}, g = sec^{2} (x y)

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

\frac{\partial}{\partial x} (x^{3}) = 3 x^{2}

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

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

\frac{\partial}{\partial x} (13 x + 6 x y^{3})

(y^{11} x) \frac{d y}{d x} = 1 + x

\int_{- \infty}^{- 1} e^{- 10 t} d t

\frac{d}{d x} (- \frac{3 x ^{2}}{2 y})

\int e^{r t} d t