How do you find the derivative of $sqrt(x - 2)$ ?

Question

1399 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-28T01:12:04

Using the chain rule.

Write as a composition of two functions:

Let your function be $f(x)$ , then $y = u^(1/2)$ and $u = x - 2$ .

The chain rule states $dy/dx = dy/(du) xx (du)/dx$ .

Differentiating y:

$y' = 1/2u^(1/2 - 1)$

$y' = 1/2u^(-1/2)$

$y' = 1/(2u^(1/2)$

Differentiating u:

$u' = 1x^(1 - 1)$

$u' = 1x^0$

$u' = 1$

Multiplying these two derivatives:

$dy/dx = 1 xx 1/(2u^(1/2)$

$dy/dx = 1/(2sqrt(x- 2))$

Hopefully this helps!

How do you find the derivative of sqrt(x - 2)sqrt(x - 2)?