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

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

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

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

- y sin (x y) sin (2 y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= sin (2 y) (- sin (x y) y)

Simplify

= - y sin (x y) sin (2 y)

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