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

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

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

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

- 2 e^{2 y} sin (2 x)

Solution steps

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

Simplify

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

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

- sin (2 x) \frac{\partial}{\partial x} (2 x)

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

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

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

Simplify

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

\frac{d}{d x} (12 cos (x))

x \to \infty lim (x^{x})

\int \frac{1 - x ^{2}}{1600} d x

x ln (x^{2})

y^{^{''}} + 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 0

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