Question

How do you differentiate `sqrt(16-x^2)`?

Answer 1

`d/dxsqrt(16-x^2)=-1/sqrt(16-x^2)`

Explanation:

diff'n of `sqrt(x)` is `d/dxx^(1/2)`
apply `n-1` rule: `1/2x^(1/2-1)\rightarrow1/2x^(-1/2)`

therefore...
`d/dxsqrt(16-x^2)`

apply chain rule
`1/2(16-x^2)^(-1/2)\timesd/dx(16-x^2)`

differentiate
`(1/(2\times(16-x^2)^(1/2)))\times-2x`

simplify:
`-1/sqrt(16-x^2)`