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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

- x^{2} cos (x y)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= - x \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

= - x cos (x y) x

Simplify

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

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

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