What is the derivative of e^{1/3 x} ?

The derivative of e^{1/3 x} is e^{x/3} 1/3

What is the first derivative of e^{1/3 x} ?

The first derivative of e^{1/3 x} is e^{x/3} 1/3

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\frac{d}{d x} (e^{\frac{1}{3} x})

e^{\frac{x}{3}} \frac{1}{3}

Solution steps

\frac{d}{d x} (e^{\frac{1}{3} x})

Simplify

e^{\frac{1}{3} x} : e^{\frac{x}{3}}

= \frac{d}{d x} (e^{\frac{x}{3}})

Apply the chain rule:

e^{\frac{x}{3}} \frac{d}{d x} (\frac{x}{3})

= e^{\frac{x}{3}} \frac{d}{d x} (\frac{x}{3})

\frac{d}{d x} (\frac{x}{3}) = \frac{1}{3}

= e^{\frac{x}{3}} \frac{1}{3}

e^{- x} - e^{- x} x

\frac{d}{d x} (e^{x - 4})

\frac{d y}{d x} = (1 + y^{2}) tan (x), y (0) = 1

x \to 1 lim (2 x)

f (x) = x^{2} - 2 x, (5, 9)

What is the derivative of e^{1/3 x} ?
The derivative of e^{1/3 x} is e^{x/3} 1/3
What is the first derivative of e^{1/3 x} ?
The first derivative of e^{1/3 x} is e^{x/3} 1/3