Question

Help me check these derivatives?

A) K=e^3r+r^5e^-.09r

My answer: 3e^3r+5r^4(e^-0.9r)*(-0.9e^-0.9r)

B) G(x)=15(0.57)^x/6

My answer: (8.55)^x/6*(.57x/6)^1-x/6

Answer 1

I think you forgot a factor of r^5 in the product rule in your first answer

Answer 2

for the second one I think you used the wrong rule

Answer 3

I used chain rule for the 2nd and first. Could you show me how you would solve them?

Answer 4

I'm sorry I have to go, but someone else will help you.

Answer 5

how do you apply chain rule ??

Answer 6

\[r^5*e^{-0.9 r}\]

Answer 7

Would I not apply chain rule for that?

Answer 8

Or would I just take the derivative of each?

Answer 9

show me your steps

Answer 10

Alright. 5r^4*(e^-.9r)*(-.9e^.-9r)

Answer 11

That's what i did...

Answer 12

r^5(z)*(z')

Answer 13

\[=U*\frac{ dV }{ dr }+V\frac{ dU }{ dr }\]

Answer 14

and take the derivative of r^5, which is 5r^4

Answer 15

first we will keep second term as it is and derivative of first than add that with derivative of second and keep first as it is

Answer 16

Why? What rule is this?

Answer 17

5r^4*e^-0.9r + ???

Answer 18

-.9e^-.9r?

Answer 19

product rule

Answer 20

So you're essentially saying the product rule is almost exactly like the chain rule except you add and not multiply?

Answer 21

you know formula for it ??

Answer 22

For the product rule? I don't think so.

Answer 23

well in product rule we only differentiate one and keep others untouched

Answer 24

r^5*e^-0.9r
they are two terms r^5 and e^-0.9r

Answer 25

choose one term which you want to differentiate ???

Answer 26

@hhipkiss pls reply

Answer 27

So, the adding would be r^5*-.9e^-.9r?

Answer 28

3e^3r+(5r^4)*(e^-.9r)+(r^5*-.9e^-.9r)?

Answer 29

a little mistake

Answer 30

Which is?

Answer 31

minus sign will come out as both term are in multiplication

Answer 32

on second part
(-r^5*9*e^-0.9r)

Answer 33

oh, yeah, gotcha.

Answer 34

Could you assist me with B possibly?

Answer 35

base is constant ..agree??

Answer 36

the 15? Yes.

Answer 37

I was thinking of maybe using A^x=(lna)(a^x)?

Answer 38

yes :)

Answer 39

15 is constant so keep it aside we will bring it later

Answer 40

(0.57)^x/6

Answer 41

what is a here ????

Answer 42

A is .57.