need to determine f'(x) of f(x)= 5e^(x/5)

Question

anonymous · Answer

is it 5e^(x/5) * ln 5((5-x)/25)?

anonymous · Answer

as f(x)= 5e^(x/5) then f'(x)=e^(x/5)

anonymous · Answer

What happened to the first 5?differentiates to 1?

hero · Answer

let u = x/5

hero · Answer

5 is just a constant. You move it out of the way, then take the derivative of e^u

anonymous · Answer

it cant be x and you dont have to do u substitution because when we differentiate 5e^(x/5)
then we get 5e^(x/5) but now we also have to differentiate x/5 also therefore we would just bring that in chain rule and bring it infront of (1/5)5e^(x/5)as a result it will be only e^(x/5) by using chain rule

anonymous · Answer

oh okay.. so thats e^(x/5)dx..

anonymous · Answer

yes u got it !!!

hero · Answer

I said let u = 1/5 to make it easier. Just trying to help :(

anonymous · Answer

haha.. Hyginkz must`ve got it.. ^_^

anonymous · Answer

hero its all koo but u just makes it worse so let it be out of it but it was a good suggestion one can do that also!!!

anonymous · Answer

ok what does u signify, I see it in my book but have not been able to make the connection...

anonymous · Answer

it is just a substitution to make problem easier in other words look fancy with no fractions involved

hero · Answer

it's just a variable substitution to make expressions easier to derivate

anonymous · Answer

ok

hero · Answer

The whole time @Mimi_x3 says nothing

anonymous · Answer

so the constant 5 gets derivitated to 1?

hero · Answer

face palm ^

mimi_x3 · Answer

Lol, i was doing it..i was slow..

anonymous · Answer

then e remains e?

anonymous · Answer

sorry this is kicking my rear

hero · Answer

There's a general rule to follow when taking the derivative of an expression with a constant affixed to it. Go and re-read that part of your text.

mimi_x3 · Answer

Use the formula..
$$\large \frac{d}{dx}  e^{ax+b}  => e^{ax+b}*a  $$
so...
$$5e^{\frac{x}{5}}   => 5e^{\frac{x}{5}}  * \frac{1}{5}  $$

anonymous · Answer

derivative of x/5 is 1/5, multiplied by the constant 5 to = 1, and e^x/5 is all that's left

anonymous · Answer

-7x^2 would be -14x right?

anonymous · Answer

yes

anonymous · Answer

OK, I think I get it.

anonymous · Answer

now to find the slope when x = a for f'(x)

anonymous · Answer

slope 1...

anonymous · Answer

Thanks

mimi_x3 · Answer

i don't understand your question..derivative of x?