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

By signing up, you agree to our Terms of Service and Privacy Policy

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}).

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

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

By signing up, you agree to our Terms of Service and Privacy Policy

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7