(\partial)/(\partial x)(y^4cos(5x))

解答

\frac{\partial}{\partial x} (y^{4} cos (5 x))

- 5 y^{4} sin (5 x)

求解步骤

\frac{\partial}{\partial x} (y^{4} cos (5 x))

将

y

视为常数

将常数提出:

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

= y^{4} \frac{\partial}{\partial x} (cos (5 x))

使用连锁律:

- sin (5 x) \frac{\partial}{\partial x} (5 x)

= - sin (5 x) \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

= y^{4} (- sin (5 x) \cdot 5)

化简

= - 5 y^{4} sin (5 x)

\int_{5}^{8} \frac{1}{9 + ( x - 5 ) ^{2}} d x

n = 1 \sum \infty 2^{n + 1} - 2^{n}

\frac{d}{d x} (\frac{( 4 x - 2 ) ^{4}}{( - 5 x + 1 ) ^{5}})

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

im pl i c i t \frac{d y}{d x}, x = y^{4}