What is (\partial)/(\partial y)(e^xcos(2y)) ?

The answer to (\partial)/(\partial y)(e^xcos(2y)) is -2e^xsin(2y)

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(\partial)/(\partial y)(e^xcos(2y))

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

y^{^{'}} + 4 y = 32 x, y (0) = 3

\frac{d y}{d x} = x y + 5 x + 4 y + 20

\frac{d}{d x} (7 e^{- 5 x})

\frac{d}{d x} (\frac{10}{e ^{x}})

f (x) = 2 x^{4}, at x = - 2, 32

What is (\partial)/(\partial y)(e^xcos(2y)) ?
The answer to (\partial)/(\partial y)(e^xcos(2y)) is -2e^xsin(2y)