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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Simplify

= 4 e^{2 y} sin (2 x)

y = x^{4} - x^{2}, y^{2} = x^{2}

y^{^{''}} - 2 y^{^{'}} + \frac{53}{4} y = 0

x \to 0 - lim (\frac{cos ( x )}{x})

\frac{d y}{d x} = \frac{( 2 x + sec ^{2} ( x ) )}{2 y}

x \to 2 + lim (\frac{x - 13}{- x + 2})

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