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

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

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

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

e^{- y} cos (x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

= e^{- y} cos (x)

\frac{d y}{d x} = \frac{2 x ^{3}}{y ^{2}}, y (2) = 3

\frac{d}{d x} (17 - x^{2} - 4 y^{2})

\int (4 - x^{2})^{3} d x

\frac{d}{d x} (\frac{( 4 x ^{2} + 4 x + 4 )}{x})

- \frac{1}{( 3 + x ) ^{2}}

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