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

The answer to (\partial)/(\partial x)(sin(2xy)) is cos(2xy)*2y

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

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

cos (2 x y) \cdot 2 y

Solution steps

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

Treat

y

as a constant

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

= cos (2 x y) \cdot 2 y

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