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When doing questions like this you simply times the top and bottom of the fraction by the bottom function but with a sign change. For example if "5 - √3" was the denominator of ...

y=(4x^2+1)^5                        y=u^5          u=4x^2+1

                                             y’=5u^4   (wrt u)  u’=8x

y’=40x(4x^2+1)^4

y’=40x(4x^2+1)^4=0             x=0  ...

In exponential form, sinh^2(x)=1/4(e^2x+e^-2x-2), cosh^2(x)=1/4(e^2x+e^-2x+2). Therefore cosh^2(x)-sinh^2(x)=1/4(2-(-2))=4/4=1, as required. 

Each part can be done separately, so x^2 becomes 2x, xy becomes dy/dx + y by product rule, y^2 becomes 2y(dy/dx) by chain rule, and 1 becomes 0. Hence the answer is 2x + y + (2y+1)dy/dx = 0, but the answe...

The Electoral College (EC) is a constitutional mechanism, better described as a process. It is used to elect the President and Vice-President. The EC was introduced as a compromise betwee...