# Differentiation using logarithmsWatch

Announcements
#1
How would I go about to working out this question

Made an attempt at it using implicit differentiation, where I used the product rule too. Just want to see if this is a right way of doing it and would reach a correct answer

Note that I also used a standard result of what dy/dx would be of y = ax , so that I didn't need to write the extra steps in my working out above

Thanks!
Last edited by Yatayyat; 3 weeks ago
0
#2
(Original post by vbzl)
Looks very good to me.
Ok cheers 👍
0
3 weeks ago
#3
(Original post by Yatayyat)
Ok cheers 👍
Your differentiation of y^x with respect to x doesn't look right. If you set z = y^x

then lnz = x lny

so 1/z dz/dx = lny + x/y dy/dx

and then go from there...
1
#4
(Original post by RichE)
Your differentiation of y^x with respect to x doesn't look right. If you set z = y^x

then lnz = x lny

so 1/z dz/dx = lny + x/y dy/dx

and then go from there...

So is the expression I need shown above when I differentiate y^x wrt x
0
3 weeks ago
#5
(Original post by Yatayyat)

So is the expression I need shown above when I differentiate y^x wrt x
Yes, that's correct.
0
#6
(Original post by ghostwalker)
Yes, that's correct.
Thanks, so I followed up from that and got my new dy/dx to be this:

0
3 weeks ago
#7
(Original post by Yatayyat)
Thanks, so I followed up from that and got my new dy/dx to be this:

Yes. And you can combine the and in the numerator into
1
3 weeks ago
#8
Also, for part a, you need to double check your differentiation.
2
#9
(Original post by simon0)
Also, for part a, you need to double check your differentiation.
Have I made a mistake when doing my product rule differentiation?
I forget to multiply by y I think

My new answer for part a) gives this now

0
3 weeks ago
#10
(Original post by Yatayyat)
Have I made a mistake when doing my product rule differentiation?
I forget to multiply by y I think

My new answer for part a) gives this now
Yep
0
#11
(Original post by RDKGames)
Yep
Thanks
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• Bournemouth University
Wed, 19 Feb '20
• Buckinghamshire New University
Wed, 19 Feb '20
• University of Warwick
Thu, 20 Feb '20

### Poll

Join the discussion

#### Have you ever accessed mental health support services at University?

Yes (44)
24.18%
No, but I have thought about it (49)
26.92%
No (89)
48.9%

View All
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.