en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(sin(nx)e^{-ny})

Solution

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

Solution

- n e^{- n y} sin (n x)

Solution steps

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

Treat

n, x

as a constant

Take the constant out:

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

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

Apply the chain rule:

e^{- n y} \frac{\partial}{\partial y} (- n y)

= e^{- n y} \frac{\partial}{\partial y} (- n y)

\frac{\partial}{\partial y} (- n y) = - n

= sin (n x) e^{- n y} (- n)

Simplify

= - n e^{- n y} sin (n x)

Popular Examples

y^{''}+11y^'+18y=0

y^{^{''}} + 11 y^{^{'}} + 18 y = 0

integral of 1/(16sqrt(x)+16x)

\int \frac{1}{16 x + 16 x} d x

tangent of y=xsqrt(x),\at x=16 tangent of

y = x x, at x = 16

limit as x approaches 3 of 10-x

x \to 3 lim (10 - x)

integral of-4e^{(-x/4)}

\int - 4 e^{(- \frac{x}{4})} d x

Frequently Asked Questions (FAQ)

What is (\partial)/(\partial y)(sin(nx)e^{-ny}) ?
The answer to (\partial)/(\partial y)(sin(nx)e^{-ny}) is -ne^{-ny}sin(nx)