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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{\partial}{\partial y} (e^{s i n (x + y)})

e^{s i n (x + y)} cos (x + y)

Solution steps

\frac{\partial}{\partial y} (e^{s i n (x + y)})

Treat

x

as a constant

Apply the chain rule:

e^{s i n (x + y)} \frac{\partial}{\partial y} (sin (x + y))

= e^{s i n (x + y)} \frac{\partial}{\partial y} (sin (x + y))

\frac{\partial}{\partial y} (sin (x + y)) = cos (x + y)

= e^{s i n (x + y)} cos (x + y)

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