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

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

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

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

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

Solution steps

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

Apply the chain rule:

- sin (n x) \frac{\partial}{\partial x} (n x)

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

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

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

Simplify

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

\int \frac{arctan ( 5 x )}{1 + 25 x ^{2}} d x

f (x) = \frac{x ^{4} + 5 x ^{2} + 10}{x ^{2}}

\int e^{x} - e^{- x} d x

x = 1 - y^{2}, x = y^{2} - 1

\frac{\partial}{\partial x} (\frac{h ( x ) c}{x})

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