Whats the derivative of 7e^(-.04x)

Question

anonymous · Answer

7(-.04)e^(-.04x)

anonymous · Answer

You're supposed to be earning chain rule.

anonymous · Answer

You keep getting people to give you the answer.  When will you try to learn?

anonymous · Answer

i dont get how to use the chain rule when they dont give u two equations:(

anonymous · Answer

if u teach me ill learn:)

e.mccormick · Answer

Ah, then what you need to see here is where the two equations are.  I can help with that.

e.mccormick · Answer

In $7e^{(-.04x)}$ you have e to some power.  e to some power is always a function in calculus.  That power of $-.04x$ is a second function. This makes it $7u^v$.  Now, e to a power is a bit special, so you see it show back up in the answer.

anonymous · Answer

then wudnt it b$$7\left( -0.04x \right)e ^{-0.04x}$$

anonymous · Answer

sry.,the x next to the 0.04 was a typo

e.mccormick · Answer

Yes, $7(-.04)e^{-.04x}$ And you can multiply the 7 by -.04 to get $-.28e^{-.04x}$

anonymous · Answer

ohhok ! thank you so much!

e.mccormick · Answer

Yah, that is a basic process you can use any time you see this format:$$ke^{f(x)}$$
The derivative of e to anyhting is exactly what was there, but when a function is in the power you put the derivative of it out front and simplify.  So:
$$f'(x)ke^{f(x)}$$becomes the solution.