What is (\partial)/(\partial x)(e^{7y}sin(-7x)) ?

The answer to (\partial)/(\partial x)(e^{7y}sin(-7x)) is -e^{7y}cos(7x)*7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(e^{7y}sin(-7x))

\frac{\partial}{\partial x} (e^{7 y} sin (- 7 x))

- e^{7 y} cos (7 x) \cdot 7

Solution steps

\frac{\partial}{\partial x} (e^{7 y} sin (- 7 x))

Simplify

e^{7 y} sin (- 7 x) : - e^{7 y} sin (7 x)

= \frac{\partial}{\partial x} (- e^{7 y} sin (7 x))

Treat

y

as a constant

Take the constant out:

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

= - e^{7 y} \frac{\partial}{\partial x} (sin (7 x))

Apply the chain rule:

cos (7 x) \frac{\partial}{\partial x} (7 x)

= cos (7 x) \frac{\partial}{\partial x} (7 x)

\frac{\partial}{\partial x} (7 x) = 7

= - e^{7 y} cos (7 x) \cdot 7

What is (\partial)/(\partial x)(e^{7y}sin(-7x)) ?
The answer to (\partial)/(\partial x)(e^{7y}sin(-7x)) is -e^{7y}cos(7x)*7