Factorising (after differentiating) (1 Viewer)

[Smile12345]

I'm not sure how to factorise this after differentiating - hopefully I've done this right.....

Q:Find the exact gradient of the tangent to the curve y=x(2x+5)^1/2 at the point where x=1...

I've differentiated to (2x+5)^1/2 + x(2x+5)^-1/2.... I think the x is wrong?

Thanks for your help in advance...

 

[spidercrab]

dont think you need to factories, just substitute x = 1 and simplify

 

[Smile12345]

dont think you need to factories, just substitute x = 1 and simplify

Answers say: (7)^1/2 + 1/(7)^1/2 = 8/(7)^1/2

Ummmm... U sure?

 

[Menomaths]

I'm not sure how to factorise this after differentiating - hopefully I've done this right.....

Q:Find the exact gradient of the tangent to the curve y=x(2x+5)^1/2 at the point where x=1...

I've differentiated to (2x+5)^1/2 + x(2x+5)^-1/2.... I think the x is wrong?

Thanks for your help in advance...

You've differentiated correctly

 

[Smile12345]

You've differentiated correctly

Very good... Thanks for confirmation... Now how do I factorise?

 

[Menomaths]

Very good... Thanks for confirmation... Now how do I factorise?

You sub in x = 1.
(2x+5)^1/2 + x(2x+5)^-1/2
This is (7^1/2) +1 /7^1/2.
Take L.C.F
8/(7^1/2)

 

[Smile12345]

You sub in x = 1.
(2x+5)^1/2 + x(2x+5)^-1/2
This is (7^1/2) +1 /7^1/2.

Thanks heaps. ... I've got this far now! But how do I get to 8/root 7???

 

[Menomaths]

Edited

 

[Smile12345]

Edited

Thanks.... How did you get 8??? Sorry seem to be having a 'dumb' moment.

 

[Menomaths]

Thanks.... How did you get 8???

When you add square root 7 + 1/square root 7, you take square root 7 as the common denominator and you add the fractions as normal.
Multiply square root 7's denominator (which is 1) by the common denominator which is square root 7 you get (square root 7)*2 which is 7. Then 7+1 = 8

 

[Smile12345]

When you add square root 7 + 1/square root 7, you take square root 7 as the common denominator and you add the fractions as normal.
Multiply square root 7's denominator (which is 1) by the common denominator which is square root 7 you get (square root 7)*2 which is 7. Then 7+1 = 8

Thanks heaps... I understand exactly... Really was having one of those moments... Please forgive me.

 

[Menomaths]

It's okay, I have a lot of those moments too.

 

[Smile12345]

It's okay, I have a lot of those moments too.

Thanks...