What is (\partial)/(\partial x)(sin(nx)e^{-ny}) ?

The answer to (\partial)/(\partial x)(sin(nx)e^{-ny}) is e^{-ny}cos(nx)n

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

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

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

Solution steps

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

Treat

n, y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

What is (\partial)/(\partial x)(sin(nx)e^{-ny}) ?
The answer to (\partial)/(\partial x)(sin(nx)e^{-ny}) is e^{-ny}cos(nx)n