Differentiation?

Question

A curve has the equation y = (x + 2) √x - 1

(i) Show that dy/dx = kx / √x - 1, where k is a constant, and state the value of k.

Ans: 3/2


Show your workings clearly...I need to understand..thanks.

Answer 1

Something's not right with either the equation or the answer you've been given.

y=(x+2)x^0.5-1
= x^1.5+2x^0.5-1

dy/dx = 1.5x^0.5+0.5*2*x^(-0.5)
= 1.5x^0.5+x^(-0.5)

This gives your k=3/2, but the differentiation gives x^(-0.5) not -1 as the rest of the answer.

Answer 2

y´= sqrt(x-1) +(x+2)*1/(2sqrt(x-1) = (2x-2 +x+2)/2sqrt(x-1)=
3/2* x/sqrt(x-1)