What is (\partial)/(\partial x)(-4y^3sin(4x)) ?

The answer to (\partial)/(\partial x)(-4y^3sin(4x)) is -16y^3cos(4x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(-4y^3sin(4x))

\frac{\partial}{\partial x} (- 4 y^{3} sin (4 x))

- 16 y^{3} cos (4 x)

Solution steps

\frac{\partial}{\partial x} (- 4 y^{3} sin (4 x))

Treat

y

as a constant

Take the constant out:

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

= - 4 y^{3} \frac{\partial}{\partial x} (sin (4 x))

Apply the chain rule:

cos (4 x) \frac{\partial}{\partial x} (4 x)

= cos (4 x) \frac{\partial}{\partial x} (4 x)

\frac{\partial}{\partial x} (4 x) = 4

= - 4 y^{3} cos (4 x) \cdot 4

Simplify

= - 16 y^{3} cos (4 x)

What is (\partial)/(\partial x)(-4y^3sin(4x)) ?
The answer to (\partial)/(\partial x)(-4y^3sin(4x)) is -16y^3cos(4x)