What is (\partial)/(\partial y)(-sin(xy)) ?

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

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(\partial)/(\partial y)(-sin(xy))

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

- cos (x y) x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= - cos (x y) x

\frac{d P}{d t} = 0.2 P - 0.001 P^{2}

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

\frac{\partial}{\partial x} (30 y^{7} x^{4} - 20 y^{6} x^{3})

\frac{d}{d x} (- 30 x^{3} + \frac{12 x}{5} - \frac{1}{3})

(2 e^{3 x})^{^{'}}

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