(\partial)/(\partial y)((sin(mx+ny))^2)

解答

\frac{\partial}{\partial y} ((sin (m x + n y))^{2})

n sin (2 (m x + n y))

求解步骤

\frac{\partial}{\partial y} ((sin (m x + n y))^{2})

将

n, m, x

视为常数

使用连锁律:

2 sin (m x + n y) \frac{\partial}{\partial y} (sin (m x + n y))

= 2 sin (m x + n y) \frac{\partial}{\partial y} (sin (m x + n y))

\frac{\partial}{\partial y} (sin (m x + n y)) = cos (m x + n y) n

= 2 sin (m x + n y) cos (m x + n y) n

使用倍角公式:

2 sin (x) cos (x) = sin (2 x)

= n sin (2 (m x + n y))

\int 2 e^{- x^{2}} d x

\frac{d}{d x} (\frac{1}{6} (2 x + 1)^{3})

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

x \to - 2 lim ((5 x + 7)^{4})

d er i v a t i v e 2^{x^{2} - 3}