Question

Let y=e^(x/9).
a) Find the differential dy.

b) Evaluate dy if x=0 and dx=−0.03.

Answer 1

do you know chain rule ?
you'll need that for part a)

Answer 2

Yeah I got the derivative e^(x/9)(1/9x-1) is this right?

Answer 3

I can't find online calculators for differentiation to check my work

Answer 4

how you got (1/9x -1) part ?

Answer 5

Sorry (1/9)x^(1/9)-1))

Answer 6

let me show you the chain rule thingy,
\(\large [e^{f(x)}]'=e^{f(x)}f'(x)\)
because derivative of e^x is just e^x
got that ?
here f(x) is just x/9

Answer 7

so you would just multiply the derivative of (x/9) (which is...?)
to e^(x/9)

Answer 8

(1/9)x^(1/9)-1))<-----from this i can see that you have done the 1/9 part correct,
but you have used x^n formula, which is not the function here, we need e^x formula here..

Answer 9

oh ok so y' would equal (x/9)e^(x/9) because I use the power rule on the e, and e doesn't really change in its derivative beside pulling down the fraction?

Answer 10

the derivative of x/9 is just 1/9
so, you'll get
\(dy=\large \dfrac{1}{9}e^{x/9}dx\)
got this ?

Answer 11

Yes so this is my total derivative of y=e^(x/9)?

Answer 12

And I would just plug in the numbers of part b into my derivative?

Answer 13

yes..,more precisely, its dy
and yes, you just plug in x=0 and dx =-0.03 here.

Answer 14

ask if any doubts anywhere :)

Answer 15

I put (1/9)e^(x/9) as my answer and the assignment tells me it's still wrong. It's an online assignment.

Answer 16

you missed out dx
(1/9)e^(x/9) dx

Answer 17

oh ok I got the problem now thank you so much

Answer 18

welcome ^_^