What is (\partial)/(\partial x)(e^{-2y}sin(2x)) ?

The answer to (\partial)/(\partial x)(e^{-2y}sin(2x)) is e^{-2y}cos(2x)*2

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(\partial)/(\partial x)(e^{-2y}sin(2x))

\frac{\partial}{\partial x} (e^{- 2 y} sin (2 x))

e^{- 2 y} cos (2 x) \cdot 2

Solution steps

\frac{\partial}{\partial x} (e^{- 2 y} sin (2 x))

Treat

y

as a constant

Take the constant out:

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

= e^{- 2 y} \frac{\partial}{\partial x} (sin (2 x))

Apply the chain rule:

cos (2 x) \frac{\partial}{\partial x} (2 x)

= cos (2 x) \frac{\partial}{\partial x} (2 x)

\frac{\partial}{\partial x} (2 x) = 2

= e^{- 2 y} cos (2 x) \cdot 2

\int \frac{9 ( x - 9 )}{( x + 5 ) ( x - 2 )} d x

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

\int_{0}^{2} (2 - x)^{2} d x

cos (x)

3 x^{2}, 18 x - 6 x^{2}

What is (\partial)/(\partial x)(e^{-2y}sin(2x)) ?
The answer to (\partial)/(\partial x)(e^{-2y}sin(2x)) is e^{-2y}cos(2x)*2