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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= cos (2 y) \frac{\partial}{\partial x} (\frac{1}{e ^{2 x}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

x \to - 3 + lim (f (x))

\frac{8 x ^{2} + 8 x + 4}{x}

\int \frac{tan ^{3} ( x )}{sec ( x )} d x

\int - u^{2} d u

\int_{0}^{7} \frac{1}{u ^{2} - 49} d u

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