(\partial)/(\partial x)(cos^6(x^2y^9))

解答

\frac{\partial}{\partial x} (cos^{6} (x^{2} y^{9}))

- 12 x y^{9} cos^{5} (x^{2} y^{9}) sin (x^{2} y^{9})

求解步骤

\frac{\partial}{\partial x} (cos^{6} (x^{2} y^{9}))

将

y

视为常数

使用连锁律:

6 (cos (x^{2} y^{9}))^{5} \frac{\partial}{\partial x} (cos (x^{2} y^{9}))

= 6 (cos (x^{2} y^{9}))^{5} \frac{\partial}{\partial x} (cos (x^{2} y^{9}))

\frac{\partial}{\partial x} (cos (x^{2} y^{9})) = - sin (x^{2} y^{9}) \cdot 2 y^{9} x

= 6 (cos (x^{2} y^{9}))^{5} (- sin (x^{2} y^{9}) \cdot 2 y^{9} x)

化简

= - 12 x y^{9} cos^{5} (x^{2} y^{9}) sin (x^{2} y^{9})

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

t a y l or cos (x), \frac{π}{2}

\frac{\partial}{\partial y} (x^{4} y - 3 x^{5} y^{2})

x \to 1 lim (x + 1)

\int x ln (3 x) d x