Question

How do you use the chain rule to differentiate `(sqrtx)^10`?

Answer 1

Using the chain rule, we get `d/dx((sqrtx)^10) = 5(sqrtx)^8`. The answer can be simplified to `5x^4` (domain: `x >= 0`)

Explanation:

Using the chain rule: `d/dx(u^10) = 10u^9 (du)/dx`

In this case, `u = sqrtx`, so we have `(du)/dx = 1/(2sqrtx)`

`d/dx((sqrtx)^10) = 10 (sqrtx)^9 (1/(2sqrtx)) = 5(sqrtx)^8`