A-LEVEL MATHS HELP! Asap

skyeforster15

Hello, I'm trying to simplify this and nothing is working. It is for part c).

(edited 1 year ago)

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Reply 1

mqb2766

Original post by skyeforster15

Hello, I'm trying to simplify this and nothing is working. It is for part c).

having a fraction with negative powers on the numerator (1/2 way down) usually causes confusion. Id have used a common denominator
12x^2(x-1)^(3/2)
and see what happens with the numerator.

Reply 2

tonyiptony

It's quite hard to read, but I think a less annoying way of doing this is to notice

\frac{dy}{dx}=\frac{1}{6}x^{-1}(x-1)^{-1/2}

Then product rule just makes lives easier.

Reply 3

ghostwalker

Original post by skyeforster15

Hello, I'm trying to simplify this and nothing is working. It is for part c).

Aside from as noted above you seem to have made an algebraic slip (not checked further than the first one).

Reply 4

davros

Original post by skyeforster15

Hello, I'm trying to simplify this and nothing is working. It is for part c).

Probably no faster than what you're doing (when you fix any slips!), but note that you could multiply both sides by 6x to get:

\displaystyle 6x\dfrac{dy}{dx} = (x-1)^{-1/2}

and then differentiate both sides w.r.t.x.

On the LHS you'll get

\displaystyle 6x\dfrac{d^2y}{dx^2} + 6\dfrac{dy}{dx}

, and on the RHS you're just differentiating a (relatively) simple function rather than a messy quotient or a product of 2 negative powers. You can then substitute your given expression for dy/dx and rearrange. This gives you another way of checking your working the way you've tried it.