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

The answer to (\partial)/(\partial y)((sin(mx+ny))^2) is nsin(2(mx+ny))

Popular >

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

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

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

Solution steps

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

Treat

n, m, x

as constants

Apply the chain rule:

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

Use the Double Angle identity:

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})

2^{x^{2} - 3}

What is (\partial)/(\partial y)((sin(mx+ny))^2) ?
The answer to (\partial)/(\partial y)((sin(mx+ny))^2) is nsin(2(mx+ny))