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} \cdot 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 x^{- 1} ln (x) d x

x \to - 3 lim (\frac{x + 3}{x + 3})

f (x) = 17 x

\int \frac{x ^{2} + 9}{x ^{2}} d x

\frac{8 t}{8 + t}

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