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

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

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

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

e^{- x} cos (y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- x) = - 1

= - cos (y) e^{- x} (- 1)

Simplify

= e^{- x} cos (y)

\int \frac{4 x ^{5}}{9 - 16 x ^{6}} d x

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

f (x) = x^{2} + 2 x - 1, (1, 2)

\int 10 (x + 1) (x^{2} + 2 x + 3)^{4} d x

\frac{d}{d x} (a r (x) cos (\frac{x + 1}{3}))

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