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

The answer to (\partial)/(\partial x)(-2e^{2y}sin(2x)) is -4e^{2y}cos(2x)

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

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

- 4 e^{2 y} cos (2 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= - 2 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

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

Simplify

= - 4 e^{2 y} cos (2 x)

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

\frac{d}{d x} (f (x) (- x))

20 x^{\frac{7}{5}} - 6 x^{\frac{2}{13}}

\int 2 e^{- 2 t} d t

x^{5}

What is (\partial)/(\partial x)(-2e^{2y}sin(2x)) ?
The answer to (\partial)/(\partial x)(-2e^{2y}sin(2x)) is -4e^{2y}cos(2x)