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This was a GCSE question in 2015. There are n sweets in a bag. 6 of them are orange, the rest are yellow. Hanna takes a random sweet from the bag and eats it. She then takes another random sweet and eats tha...

You would use the product rule. uv'=uv- u'vdx. In this case we would allocate u= ln x and v'=1 so u'=1/x and v=x so uv=xlnx whilst u'v=x/x=1 so we would have xln(x) -1dx. Next we would get xln(x)-x +c

Option 1 - Differentiate using product rule giving dy/dx = cos 2 (x) - sin 2 (x). (2 marks) Subbing in x as pi (1 mark) then gives (-1) 2 + (0) 2 . Therefore the gradient is 1 (1 mark) . Option 2 - Initially...

let us start by taking two points on the curve y=x 2 , the first with x-coordinate x, and the second x+Δx and drawing a straight line between them. We can form a right-angled triangle, with two sides paralle...

Write out the question fully like so: =(x-7)(x-7) 2. Expand the brackets using the FOIL method. i.e First Outer Inner Last or the Crab Claw Method You should get: = x^2 - 7x - 7x + 49 Be careful with signs, ...