What is the derivative of y=e^{1/2 x} ?

The derivative of y=e^{1/2 x} is e^{x/2} 1/2

What is the first derivative of y=e^{1/2 x} ?

The first derivative of y=e^{1/2 x} is e^{x/2} 1/2

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derivative of

y = e^{\frac{1}{2} x}

e^{\frac{x}{2}} \frac{1}{2}

Solution steps

\frac{d}{d x} (e^{\frac{1}{2} x})

Simplify

e^{\frac{1}{2} x} : e^{\frac{x}{2}}

= \frac{d}{d x} (e^{\frac{x}{2}})

Apply the chain rule:

e^{\frac{x}{2}} \frac{d}{d x} (\frac{x}{2})

= e^{\frac{x}{2}} \frac{d}{d x} (\frac{x}{2})

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

= e^{\frac{x}{2}} \frac{1}{2}

x \to a lim (\frac{f ( x )}{p ( x )})

y = 3 - x, y = 2 x^{2}, 0, 1

\int 1 + 2 y d y

x \to 1 lim (sin (- 3 π x))

\frac{\partial}{\partial y} (\frac{x y}{x - y})

What is the derivative of y=e^{1/2 x} ?
The derivative of y=e^{1/2 x} is e^{x/2} 1/2
What is the first derivative of y=e^{1/2 x} ?
The first derivative of y=e^{1/2 x} is e^{x/2} 1/2