How do you find the derivative of #e^(1/(2x))#?

Answer 1
Use #d/(dx)(e^x)=e^x# togerther with the chain rule to see that:
#d/(dx)(e^(1/(2x)))=e^(1/(2x))*d/(dx)( 1/(2x))#
#=e^(1/(2x))* (-1/(2x^2))= -e^(1/(2x))/(2x^2)#
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Answer 2

To find the derivative of (e^{1/(2x)}), we can use the chain rule. The function (e^{1/(2x)}) is a composite function with the outer function being (e^x) and the inner function being (\frac{1}{2x}).

  1. Differentiate the outer function: (\frac{d}{dx}(e^x) = e^x).
  2. Differentiate the inner function using the chain rule: (\frac{d}{dx}\left(\frac{1}{2x}\right) = -\frac{1}{2x^2}).
  3. Apply the chain rule: Multiply the derivative of the outer function by the derivative of the inner function.
  4. The derivative of (e^{1/(2x)}) with respect to (x) is (e^{1/(2x)} \cdot \left(-\frac{1}{2x^2}\right)).
  5. Simplify the expression if necessary.

So, the derivative of (e^{1/(2x)}) with respect to (x) is (-\frac{e^{1/(2x)}}{2x^2}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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