What is (\partial)/(\partial x)(y(1-e^{-x})) ?

The answer to (\partial)/(\partial x)(y(1-e^{-x})) is e^{-x}y

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(\partial)/(\partial x)(y(1-e^{-x}))

\frac{\partial}{\partial x} (y (1 - e^{- x}))

e^{- x} y

Solution steps

\frac{\partial}{\partial x} (y (1 - e^{- x}))

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (1 - e^{- x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= y (\frac{\partial}{\partial x} (1) - \frac{\partial}{\partial x} (e^{- x}))

\frac{\partial}{\partial x} (1) = 0

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

= y (0 - (- e^{- x}))

Simplify

= e^{- x} y

What is (\partial)/(\partial x)(y(1-e^{-x})) ?
The answer to (\partial)/(\partial x)(y(1-e^{-x})) is e^{-x}y