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This is a nice little question off the 2018 Edexcel Higher Maths paper! When we heard the word 'prove' in a question at this level, automatically we should be thinking about using algebra to help us out! ...

We use the product rule with u=x and v=ln(x) (so u'=1 andv'=1/x) to differentiate xln(x) to ln(x)+1, and -x just differentiates to -1, hence we have. f'(x)=ln(x).
Now note that ln(x^3)=3ln(x) using p...

x=1, y=2
x=-2/5, y=-11/5

1. 36^1/2
   = 6(The square root of 36 is 6)
   2) 23⁰
   = 1(Anything to the power of 0 is 1)
   3) 27^-2/3
   = 3^-2 = 1/3²= 1/9
...

Use Pythagoras' theorem. a² + b² = c². The longest side of the triangle is the hypotenuse, and it is the side opposite the right angle. We use the length of this side as '...