Further gcse dy/dx

[winter plover]

Yo

[torn warren]

yi

yo

[winter plover]

So you can actually simplify that fraction

[torn warren]

ok

factor out x?

[winter plover]

Even more

You can factor out x^4

Can you then use that to deal with the denominator a bit

[torn warren]

oh ok

so x^4(x^4)

and 2(x^4)

cancel them out?

then we have 3x^9 + x^4

[winter plover]

Well you need to factor x^4 out of everything in the numerator

[torn warren]

so the 6x^9 aswell

[winter plover]

So like x^4(6x^5 + x^4)

Yeah

[torn warren]

so its gonna be 3x^5 + x^4

[winter plover]

When cancelling or simplifying you need to do it to everything

[torn warren]

when simplified

[winter plover]

Not quite

[torn warren]

then you differintiate and sub x?

[winter plover]

Your issue now is the /2

[torn warren]

ok

[winter plover]

(6x^5 + x^4)/2 isn’t the same as (6x^5)/2+ x^4

You need to keep everything divided by 2

But then yeah differentiate twice

[torn warren]

(6x^5 + x^4)/2

then what after this

differentiate?

[winter plover]

Differentiate twice

[torn warren]

ok

how do u differiante fractions

like x^4/2

[winter plover]

So because /2 is a constant you can just leave it in

Same as differentiating 1/2 * x^4

[torn warren]

oh so x^4/2 differintiated is 4x^3/2

?

[winter plover]

Yep

Which is obviously 2x^3

[torn warren]

yh

[winter plover]

Yep perfect

So do that twice and to verything

[torn warren]

then once ive done that sub in the 0.5?

[winter plover]

Yep exactly

[torn warren]

ok thank you alot for that

[winter plover]

No worries!

[torn warren]

wait

@winter plover why are differnitaing twice

[winter plover]

Because you want d^2 y / dx^2

Differentiating once just gives you dy/dx

[torn warren]

is that what the notation means

[winter plover]

Yep

[torn warren]

ok thank you for claryfing that

[winter plover]

d^2 y / dx^2 = “second derivative”

[torn warren]

oh ok

[winter plover]

Aka differentiated twice