# Thread: derivative of an exponential e

1. ## derivative of an exponential e

Little help please, my answer doesn't check out. need to find the derivative

Problem is e to x-1 / 3x2 -4

thats e to the x-1, divided by 3x squared - 4

I got -6xe to the x-1 divided by 3x squared - 4

(how do you write exponents on this forum)

2. $\displaystyle \frac{d}{dx} (e^u) = e^u \cdot \frac{du}{dx}$

where $\displaystyle u = \frac{x-1}{3x^2 - 4}$

can you find $\displaystyle \frac{du}{dx}$ ?

3. minus 6x squared minus 6x - 4 / (3x squared -4)squared, but what happened to the E?

4. oppps meant minus 3xsquared -6x-4

5. $\displaystyle \frac{d}{dx} \left[\frac{x-1}{3x^2-4}\right]$

$\displaystyle \frac{(3x^2-4)(1) - (x-1)(6x)}{(3x^2-4)^2}$

$\displaystyle \frac{du}{dx} = -\frac{3x^2 - 6x + 4}{(3x^2-4)^2}$

so ...

$\displaystyle \frac{d}{dx} (e^u) = e^u \cdot \frac{du}{dx} = -e^{\frac{x-1}{3x^2-4}} \cdot \frac{3x^2 - 6x + 4}{(3x^2-4)^2}$

6. Thank you, I guess I tried to simplify too much.. I am curious about the plus 4 in the numerator. Shouldn't that be a minus 4?

Also are you using a separate program to write the math equations and then pasting it into your reply?