What is (\partial)/(\partial x)(-2ye^{-x}) ?

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

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(\partial)/(\partial x)(-2ye^{-x})

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

2 e^{- x} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= - 2 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

= - 2 y e^{- x} (- 1)

Simplify

= 2 e^{- x} y

\int - sin (x) - cos (x) d x

y^{^{''}} - 2 y^{^{'}} - 15 y = - 2

\frac{\partial}{\partial x} (\frac{3 y ^{2} - x ^{2}}{y ^{5}})

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

\frac{d}{d x} (\frac{4 x ^{2} + 8 x + 4}{x})

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