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

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

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

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

2 y^{3} cos (y x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

t \to 0 lim (t ln (t))

\frac{d}{d x} (90 + 45 cos (\frac{x ^{2}}{18}))

\frac{\partial}{\partial y} (5 x e^{x^{2}} + y^{2})

x \to 0 lim (\frac{x ^{2} - 2 x}{x})

\frac{d}{d x} (3 x^{2} - 4)

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