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

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

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

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

- sin (2 x y) \cdot 2 y

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

3 x^{2} y d x + x^{3} d y = 0

\int_{0}^{2} e^{6 x} d x

\int - cos (5 x) d x

\frac{x ^{2} + x}{x ^{2} + 4 x}

\frac{d y}{d x} = (\frac{2 x ( y - 1 )}{x ^{2} + 3}), y (1) = 9

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