Search over 10,000 free study notes

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...

Phenyl amine is the weakest base- the benzene group has a negative inductive effect on the lone pair on the nitrogen. Therefore it is less availiable for donation.

Methyl amine is the strongest- th...