What is (\partial)/(\partial x)(y^2cos(yx)) ?

The answer to (\partial)/(\partial x)(y^2cos(yx)) is -y^3sin(yx)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(y^2cos(yx))

\frac{\partial}{\partial x} (y^{2} cos (y x))

- y^{3} sin (y x)

Solution steps

\frac{\partial}{\partial x} (y^{2} cos (y x))

Treat

y

as a constant

Take the constant out:

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

= y^{2} \frac{\partial}{\partial x} (cos (y x))

Apply the chain rule:

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

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

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

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

Simplify

y^{2} (- sin (y x) y) : - y^{3} sin (y x)

= - y^{3} sin (y x)

What is (\partial)/(\partial x)(y^2cos(yx)) ?
The answer to (\partial)/(\partial x)(y^2cos(yx)) is -y^3sin(yx)