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

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

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

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

- x y cos (x y) - sin (x y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x y), g = y

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

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

\frac{\partial}{\partial y} (y) = 1

= - (cos (x y) x y + 1 \cdot sin (x y))

Simplify

= - x y cos (x y) - sin (x y)

\int (1 - 2 x)^{\frac{3}{2}} d x

x \to 0 lim (x^{2} - x^{4})

\frac{\partial}{\partial x} (6 x y - 2 + 10 x^{2} y^{2})

\frac{\partial}{\partial x} (x arctan (y + z))

f (x) = \frac{x}{- 6 x + 6}, at x = 2

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