What is (\partial)/(\partial x)(-e^{8y}cos(8x)*8) ?

The answer to (\partial)/(\partial x)(-e^{8y}cos(8x)*8) is 64e^{8y}sin(8x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(-e^{8y}cos(8x)*8)

\frac{\partial}{\partial x} (- e^{8 y} cos (8 x) \cdot 8)

64 e^{8 y} sin (8 x)

Solution steps

\frac{\partial}{\partial x} (- e^{8 y} cos (8 x) \cdot 8)

Treat

y

as a constant

Take the constant out:

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

= - e^{8 y} \cdot 8 \frac{\partial}{\partial x} (cos (8 x))

Apply the chain rule:

- sin (8 x) \frac{\partial}{\partial x} (8 x)

= - sin (8 x) \frac{\partial}{\partial x} (8 x)

\frac{\partial}{\partial x} (8 x) = 8

= - e^{8 y} \cdot 8 (- sin (8 x) \cdot 8)

Simplify

= 64 e^{8 y} sin (8 x)

What is (\partial)/(\partial x)(-e^{8y}cos(8x)*8) ?
The answer to (\partial)/(\partial x)(-e^{8y}cos(8x)*8) is 64e^{8y}sin(8x)