What is the first derivative of ye^x ?

The first derivative of ye^x is e^x

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derivative of ye^x

derivative of

y e^{x}

e^{x}

Solution steps

\frac{d}{d y} (y e^{x})

Treat

x

as a constant

Take the constant out:

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

= e^{x} \frac{d y}{d y}

Apply the common derivative:

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

= e^{x} \cdot 1

Simplify

= e^{x}