What is (\partial)/(\partial y)(x^2sin^2(y)) ?

The answer to (\partial)/(\partial y)(x^2sin^2(y)) is x^2sin(2y)

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(\partial)/(\partial y)(x^2sin^2(y))

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

x^{2} sin (2 y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= x^{2} \frac{\partial}{\partial y} (sin^{2} (y))

Apply the chain rule:

2 sin (y) \frac{\partial}{\partial y} (sin (y))

= 2 sin (y) \frac{\partial}{\partial y} (sin (y))

\frac{\partial}{\partial y} (sin (y)) = cos (y)

= x^{2} \cdot 2 sin (y) cos (y)

Use the Double Angle identity:

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

= x^{2} sin (2 y)

\frac{d}{d x} (1^{\frac{1}{3}})

x^{2} y^{^{''}} + 3 x y^{^{'}} + y = \frac{1}{x}

\frac{d}{d x} ((e^{x}) (cos (x)))

(6.1) (1.1)

(2 x + y + 1) (\frac{d y}{d x}) = 1

What is (\partial)/(\partial y)(x^2sin^2(y)) ?
The answer to (\partial)/(\partial y)(x^2sin^2(y)) is x^2sin(2y)