What is (\partial)/(\partial y)(cos(nx)e^{ny}) ?

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

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

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

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

Solution steps

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

Treat

n, x

as a constant

Take the constant out:

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

= cos (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

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

\int \frac{9}{x ^{2} x ^{2} + 36} d x

\int sin (4 x) sin (2 x) d x

x \to - 1 lim (\frac{x}{x ^{2} - 1})

\frac{x ^{3} + 3 x}{x ^{2} - 4 x + 3}

x \to 4 - lim (\frac{∣ x - 4 ∣}{x - 4})

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