Find StartFraction dy Over dx EndFraction for y equals StartRoot u EndRoot and u equals x squared plus 1.

Question

asked Jan 3, 2021 174k views

1 Answer

Lork · Answer 1 · 2021-01-07T02:03:17+0000

Answer:

$(dy)/(dx)=\frac{x}{\sqrt {x^2+1}}$

Explanation:

We want to find:

$(dy)/(dx) \\y=\sqrt u\\(d)/(dx)(√(u))$

Given that:

u=x^2+1

Applying the chain rule:

(dy)/(dx)=(dy)/(du)*(du)/(dx)

Solving dy/du:

$(dy)/(du)=(d)/(du)(\sqrt u)\\(dy)/(du)=(1)/(2\sqrt u)$

Solving du/dx:

(d)/(dx)(x^2+1) = 2x

Therefore, dy/dx is determined by:

$(dy)/(dx)=(1)/(2\sqrt u)*2x \\(dy)/(dx)=(x)/(\sqrt u)\\(dy)/(dx)=\frac{x}{\sqrt {x^2+1}}$