(\partial)/(\partial x)((9+20x)y^{tan(x)})

解答

\frac{\partial}{\partial x} ((9 + 20 x) y^{t a n (x)})

20 y^{t a n (x)} + y^{t a n (x)} ln (y) sec^{2} (x) (9 + 20 x)

求解步骤

\frac{\partial}{\partial x} ((9 + 20 x) y^{t a n (x)})

将

y

视为常数

使用微分乘法定则:

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

f = 9 + 20 x, g = y^{t a n (x)}

= \frac{\partial}{\partial x} (9 + 20 x) y^{t a n (x)} + \frac{\partial}{\partial x} (y^{t a n (x)}) (9 + 20 x)

\frac{\partial}{\partial x} (9 + 20 x) = 20

\frac{\partial}{\partial x} (y^{t a n (x)}) = y^{t a n (x)} ln (y) sec^{2} (x)

= 20 y^{t a n (x)} + y^{t a n (x)} ln (y) sec^{2} (x) (9 + 20 x)

t an g e n t f (x) = - x^{2}, (- 3, - 9)

\int \frac{2}{( x - 2 ) ( x ^{4} + 4 )} d x

x \to - \infty lim (- 3 - x)

\int_{0}^{3} x^{2} + 16 d x

\frac{d y}{d x} + \frac{y}{x} = \frac{- y ^{2}}{x}