Question

CHECK MY ANSWER?
find the derivative of 5^(-4x)

I got -4x(ln5)5^(-4x-1)

Answer 1

This is incorrect. The derivative of \[a^x\] for a constant\[a\] is \[a^x\ln{(a)}\] Since you have something other than just \[x\] as an exponent, you need to use the Chain Rule.
The derivative in this case will be of the form \[\frac{d}{dx}a^{u}=a^{u}\ln{(a)}\cdot \frac{du}{dx}\] of course \[a=5\] and \[u=-4x\] in your problem

Answer 2

so its 4(ln5)5^(-4x)?

Answer 3

Almost. You are missing a minus sign from the derivative of \[-4x\] Put that out front and you've got it.

Answer 4

i know and thats what confused me but the answer choices are:
4(ln5)5^(-4x)
-4(ln5)5^(-4x-1)
4(ln5)5^(5x)
(-4ln5)/(625^x)

Answer 5

Man I hat these type of questions. All they have done is to rewrite \[5^{-4x}\] as \[(5^{-4})^x=(\frac{1}{5^4})^x=\frac{1}{625^x}\] This obscures the real issue of calculating a derivative. The solution is of course the last one

Answer 6

ok thanks!

Answer 7

No problem