What is the derivative of e^{kx} ?

The derivative of e^{kx} is e^{kx}k

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

The first derivative of e^{kx} is e^{kx}k

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

e^{k x} k

Solution steps

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

Apply the chain rule:

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

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

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

= e^{k x} k

What is the derivative of e^{kx} ?
The derivative of e^{kx} is e^{kx}k
What is the first derivative of e^{kx} ?
The first derivative of e^{kx} is e^{kx}k