What is (\partial)/(\partial x)(e^{-2x}cos(-3y)) ?

The answer to (\partial)/(\partial x)(e^{-2x}cos(-3y)) is -2e^{-2x}cos(3y)

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(\partial)/(\partial x)(e^{-2x}cos(-3y))

\frac{\partial}{\partial x} (e^{- 2 x} cos (- 3 y))

- 2 e^{- 2 x} cos (3 y)

Solution steps

\frac{\partial}{\partial x} (e^{- 2 x} cos (- 3 y))

Simplify

e^{- 2 x} cos (- 3 y) : e^{- 2 x} cos (3 y)

= \frac{\partial}{\partial x} (e^{- 2 x} cos (3 y))

Treat

y

as a constant

Take the constant out:

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

= cos (3 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 (3 y) e^{- 2 x} (- 2)

Simplify

= - 2 e^{- 2 x} cos (3 y)

\frac{d}{d x} (arcsin (\frac{x ^{2} - 1}{x ^{2}}))

f (x) = \frac{3}{x ^{7}}

\int 2 t d t

\frac{d}{d x} (\frac{x ^{2} - 1}{x + 2})

\frac{d y}{d x} = x y + x + y + 1

What is (\partial)/(\partial x)(e^{-2x}cos(-3y)) ?
The answer to (\partial)/(\partial x)(e^{-2x}cos(-3y)) is -2e^{-2x}cos(3y)