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(Note: in this answer I will use the notation y' to represent the differential of y, and by the same reasoning y'' denotes the differential of y', or the second derivative of y.) A curve's maximum or minimum...

the aim of finsing the inverse is making x the subject. To start we need to multiply both sides by: (x-1), giving us:y(x-1) = 2x+1now we need to expand the brackets:yx - y = 2x+1now gather all the x componen...

To find the inverse we're wanting to make x the subject. First start by multiplying both sides by (x-1), this gives us y(x-1) = 2x+1. Expand the brackets giving yx - y = 2x+1. Gather all the x components ont...

Y=(2x-3)/x 2 Quotient Rule: dY/dx(u/v)=(u'v-v'u)/v 2 dY/dx=(2x 2 -2x(2x-3))/x 4 =(6x-2x 2 )/x 4 (Collect numerator x terms.) =(6-2x)/x 3 (Cancel the fraction by a factor of x.) dY/dx=(6-2x)/x 3

First write cosh and sinh as exponentials, from their respective definitions:sinh x = 1/2 (e x - e -x )cosh x = 1/2 (e x + e -x ​)So: 3 * 1/2 (e x + e -x ​) - 4 * 1/2 (e x - e -x ) = 7Multiply by 2: 3 * (e x...