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

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

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

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

- x^{2} sin (x y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x (- sin (x y) x)

Simplify

x (- sin (x y) x) : - x^{2} sin (x y)

= - x^{2} sin (x y)

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

\frac{7}{ln ( x )}

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

\int (4 x^{3} + 3 x^{2} + 2 x + 1) d x

\frac{1}{t}

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