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Answer is 2x - 4. This is found by following the standard differentiation procedure of n(ax-b)^n-1 where n was the previous power and a and b are the value inside the bracket. This means that it first goe...

Expand to get xy+3y-4x-12=x^2+y^2Rearrange to xy+3y-4x-12-x^2-y^2
Then you have to differentiate implicitly:
use product rule on xy to get:u = x v =ydu = 1 dv = dy/dx
so xy differentiates t...

1. Substitute f(x) = 53 into the equation given:f(x) = 53 = 2x² + 32).
   
   2. Rearrange to get x² on the left hand side: x² = (53-3)/2 = 253).
   
   3. Sq...

Indices are often referred to as powers of a number. A power of a number is the number of times you multiply that number by itself. The indices laws are the rules for how these numbers can be manipulated ...

First, we factorize each number.150=(5^2)32 and 100=(2^2)*(5^2) then to calculate the highest common factor we take the common factors with the smallest powers. In this case (5^2) and 2. That mea...