C4 parametric differentiation

There are two questions from my textbook where my answers are different to those in the back of the back but I can't see any mistakes. The question is find dy/dx

The first is: x=t^2 - 2t
y=t^4 - 4t

My answer is (2t^3-2)/(t-1)
Book says 2(t^2+t+1)


The second question is x=cos(t)
y=4t - tsin(t)

I got tcot(t) - 4cosec(t) but the book has got a +1 on this

Can someone please check whether the answers in the back of the book are correct because this textbook is notorious for having wrong answers.

Many thanks

1st one - you're right2nd one - the book's right.

for the second one I got tcost+sint-4/sint

The answer in the book for the first question is correct. They've just done polynomial division to tidy up your fraction .

Hmm it must be my differentiating of cos and sin

differential of cos(t) is -sin(t) yes?
and the differential of 4t-tsin(t) is 4-tcos(t)?

ahhh thank you

for the differential of 4t-tsint differentiate tsint using product rule which will give you tcost-sint so overall 4-tcost-sint

You're welcome!

You have to use the product rule to differentiate tsint it isn't just tcost.