Differentiation (1 Viewer)

[coyazayo]

Hi everyone!

Find dy/dx

1. xy-2=0

2.x/y+4x=1

3.x^2y^3+xy^2-8=0

 

[eyeseeyou]

Hi everyone!

Find dy/dx

1. xy-2=0

2.x/y+4x=1

3.x^2y^3+xy^2-8=0

1. xy-2=0
xy=2
y=2/x
y=2 times 1/x
dy/dx=-2/(x^2)

2.x/y+4x=1
x+4xy=y
x=y-4xy
x=y(1-4x)
y=x/(1-4x)
dy/dx=...
Use product rule or quotient rule to finish the rest

3. That's unclear to me. I think you need to use logs

 

[InteGrand]

Hi everyone!

Find dy/dx

1. xy-2=0

2.x/y+4x=1

3.x^2y^3+xy^2-8=0

1) Since y = 2/x, we have y' = -2/x^2.

2) Note y = x/(1-4x). Now we can use the quotient rule to get y' .

3)

 

[eyeseeyou]

1) Since y = 2/x, we have y' = -2/x^2.

2) Note y = x/(1-4x). Now we can use the quotient rule to get y' .

3)

Oh yeah it was implicit. Shit my bad :/

 

[LC14199]

What level of differentiation is this? 3U or 4U?

 

[InteGrand]

Implicit differentiation is only part of the HSC 4U syllabus.

 

[si2136]

Implicit differentiation is only part of the HSC 4U syllabus.

Could you use it in 3U?

 

[InteGrand]

Could you use it in 3U?

Yeah (pretty sure)

 

[eyeseeyou]

I'm pree sure implicit is part of 3U, you use it in 4U for conics (apparently you do)

 

[fluffchuck]

I'm pree sure implicit is part of 3U, you use it in 4U for conics (apparently you do)

You use implicit in conics to derive equations of tangents and normals to hyperbolas or ellipses.

 

[braintic]

I'm pree sure implicit is part of 3U, you use it in 4U for conics (apparently you do)

It's not mentioned in the 3U syllabus, but you can still use it and I'm pretty sure most teachers teach it.

 

[si2136]

It's not mentioned in the 3U syllabus, but you can still use it and I'm pretty sure most teachers teach it.

It's really powerful and simple.

How about the Square Root Function Rule?

 

[leehuan]

It's really powerful and simple.

How about the Square Root Function Rule?

What rule is this?

 

[si2136]

What rule is this?

It's where if you differentiate a square root function, it's

(u')/2*sqrt*f(u)

 

[InteGrand]

That's an application of the chain rule.

 

[si2136]

That's an application of the chain rule.

What I meant was that could I just write that immediately without showing working out?

 

[InteGrand]

What I meant was that could I just write that immediately without showing working out?

Pretty sure you are allowed to use the chain rule by inspection, aren't you (depends on the question maybe)? You can write "chain rule" in brackets as a reason.

 

[kashkow]

Implicit differentiation is only part of the HSC 4U syllabus.

I'm pree sure implicit is part of 3U, you use it in 4U for conics (apparently you do)

You use implicit in conics to derive equations of tangents and normals to hyperbolas or ellipses.

It's not mentioned in the 3U syllabus, but you can still use it and I'm pretty sure most teachers teach it.

It's really powerful and simple.

What is it? I've never heard of this before in 3U. Can somebody plz teach me/link me a resource to learn it?

 

[Squar3root]

It's really powerful and simple.

How about the Square Root Function Rule?

It's where if you differentiate a square root function, it's

(u')/2*sqrt*f(u)

huehuehuehue

That's an application of the chain rule.

yeah I did that many times and my teacher said it was okay. Youre using substitution technically

 

[Dettol]

What is it? I've never heard of this before in 3U. Can somebody plz teach me/link me a resource to learn it?

google is a start