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

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

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(\partial)/(\partial y)(xcos(xy))

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

- x^{2} sin (x y)

Solution steps

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

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 y}{d t} = \frac{( 4 t y ^{2} )}{t ^{2} + 1}, y (0) = \frac{1}{4}

\int x^{2} - 4 x - 5 d x

y = 9 - x^{2}, - 1 \leq x \leq 1

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

\frac{d}{d x} (9 x - 18)

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