What is the derivative of e^{tx} ?

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

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

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

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

e^{t x} t

Solution steps

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

Treat

t

as a constant

Apply the chain rule:

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

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

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

= e^{t x} t

\int_{4}^{9} 4 x d x

\frac{\partial}{\partial x} (x^{2} \frac{1}{a ^{2}})

\int \frac{13 x ^{3}}{7 + x ^{2}} d x

\int (3 x^{2} + 4 x - 4) d x

\frac{d}{d x} (csc (6 x))

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