What is the derivative of e^{xt} ?

The derivative of e^{xt} is e^{xt}t

What is the first derivative of e^{xt} ?

The first derivative of e^{xt} is e^{xt}t

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

e^{x t} t

Solution steps

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

Treat

t

as a constant

Apply the chain rule:

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

= e^{x t} \frac{d}{d x} (x t)

\frac{d}{d x} (x t) = t

= e^{x t} t

What is the derivative of e^{xt} ?
The derivative of e^{xt} is e^{xt}t
What is the first derivative of e^{xt} ?
The first derivative of e^{xt} is e^{xt}t