What is (\partial)/(\partial y)(cos(xy)y) ?

The answer to (\partial)/(\partial y)(cos(xy)y) is -xysin(xy)+cos(xy)

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(\partial)/(\partial y)(cos(xy)y)

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

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

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

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

f = cos (x y), g = y

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

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

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

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

Simplify

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

11 x - 4 y x^{2} + 1 y^{^{'}} = 0, y (0) = 10

\int (5 x^{2} + 3) d x

\frac{d}{d x} (\frac{cos ( x )}{sin ^{2} ( x )})

x \to 0 lim (x \cdot e^{\frac{1}{x}} - 1)

\frac{d y}{d x} = \frac{y ( ln ( 5 y ) - ln ( 5 x ) + 7 )}{7 x}

What is (\partial)/(\partial y)(cos(xy)y) ?
The answer to (\partial)/(\partial y)(cos(xy)y) is -xysin(xy)+cos(xy)