A level Maths OCR question help

I am doing a question where I have to prove that 5(x^2-2)(4x+9)^1/2 can be written as k(5x^2+9x-2)/(4x+9)^1/2 where k is a constant

my problem is that the equation they want me to prove looks like quotient rule but the first equation isn't a fraction...if that makes sense

Its a product so differentiate using that rule.

but if i do that i wont get (4x+9)^1/2 as the denominator

Guess youve not tried it? Derivative of 2x^(1/2) is 1/x^(1/2)

i dont mean to be stupid but where are u getting 2x^1/2 from

Just a simple example. Just try using the product rule and see how it goes.

i tried product rule and got 5x^3+70/3x^2+20x-20/3😭😭

Youll have to show your working, as thats obviously wrong.

i’ve probably made a stupid mistake tbh

Cant see the image unfortunately, image uploading has been even more flakey after the recent upgrades.

WHen you evaulate v' you seem to forget that its (4x+9)^(-1/2) on the second line of working. Thats the reason you get a sqrt(4x+9) on the deonominator.

so i have to use quotient rule inside of product rule basically?

No. Firstly, the quotient rule is a special case of the product rule, but here you use the product rule properly. Here you have
v = (4x+9)^(1/2)
v' = 2 (4x+9)^(-1/2) = 2/(4x+9)^(1/2)