What is the derivative of (t(e^{xt})) ?

The derivative of (t(e^{xt})) is e^{tx}t^2

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

The first derivative of (t(e^{xt})) is e^{tx}t^2

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

e^{t x} t^{2}

Solution steps

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

Treat

t

as a constant

Take the constant out:

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

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

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

= t e^{x t} t

Simplify

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

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

2 (x + 2)^{2} - 17 (x + 2) - 9

7^{m + 1} - 7^{m}

sin (h^{3}) (4 t)

2 x - 3 x y - 4 x + 6 y

y (ln (x))

What is the derivative of (t(e^{xt})) ?
The derivative of (t(e^{xt})) is e^{tx}t^2
What is the first derivative of (t(e^{xt})) ?
The first derivative of (t(e^{xt})) is e^{tx}t^2