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x(x+1) - x(x-1)/(x-1)(x+1)x²+x-x²+x/(x-1)(x+1)2x/x²+x-x-12x/(x²-1)

First differentiate the equation: dy/dx = 6x^2 - 6xSet this equal to 0 as at turning points the change in gradient is 0: 0 = 6x^2 - 6x6x(x-1)=06x=0 therefore x=0(x-1)=0 therefore x=1x=1,0Now substitute ba...

13y - 5 = 9y + 27 First we must collect all similar terms together on either side of the equation: 13y - 9y = 27 + 5. As you can see, if a term is moved to the other side of the equation, the opposite sig...

(x+2)(x-1)=0 x+2=0x= -2x-1=0x=1

The key to this problem is to apply sec to both sides, and then differentiate implicitly: sec(y)=x; dsec(y)/dx = 1; tan(y)sec(y)dy/dx = 1; dy/dx = 1/(tan(y)sec(y)). Then using the fact that sec(y)=x and t...