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For part i) we use the basic method of differentiation by considering each term individually. The first term, x³ goes to 3x² by multiplying the original term by the original power, b...

Rearrange the terms and group: Numbers: (3*1) =3, a variables: a * (a^3) --> (1+3=4) Therefore (a^4); b variables: (b^2)*b --> (2+1=3) Therefore (b^3); Regroup: 3(a^4)(b^3)

First you must write the function in terms on something you know how to differentiate, for example... by taking tan (..) of both sides the equation becomes, tan(y)= ax² +b. We then use implicit...

x=2t --> t= x/2 
y=t² = (x/2)². 

So the Cartesian equation is y=x²/4. 

3x+7 = 1. We can describe this equation as a stroy. First x was multiplied by 3 and then 7 was added to it to get 1. Now we need to reverse the story. 
last thing done was +7, so reversing it gives ...