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

The answer to (\partial)/(\partial x)(y^2sin(2xy)) is 2y^3cos(2yx)

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

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

2 y^{3} cos (2 y x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

cos (2 x y) \frac{\partial}{\partial x} (2 x y)

= cos (2 x y) \frac{\partial}{\partial x} (2 x y)

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

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

Simplify

y^{2} cos (2 x y) \cdot 2 y : 2 y^{3} cos (2 y x)

= 2 y^{3} cos (2 y x)

x \to - 3 lim (\frac{x + 2}{x ^{2} - 9})

\frac{z + 1}{z - 1}

\frac{1}{3 s + 4}

\int \frac{4}{x ^{2} x ^{2} + 36} d x

y^{^{''}} - 8 y^{^{'}} + 19 y = 0, y (0) = - 4, y^{^{'}} (0) = 2

What is (\partial)/(\partial x)(y^2sin(2xy)) ?
The answer to (\partial)/(\partial x)(y^2sin(2xy)) is 2y^3cos(2yx)