What is (\partial)/(\partial x)(te^{xt}) ?

The answer to (\partial)/(\partial x)(te^{xt}) is e^{tx}t^2

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(\partial)/(\partial x)(te^{xt})

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

e^{t x} t^{2}

Solution steps

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

Treat

t

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= t e^{x t} t

Simplify

t e^{x t} t : e^{t x} t^{2}

= e^{t x} t^{2}

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What is (\partial)/(\partial x)(te^{xt}) ?
The answer to (\partial)/(\partial x)(te^{xt}) is e^{tx}t^2