what is the derivative of a square root
The derivative of a square root follows one simple pattern:
- For f(x)=xf(x)=\sqrt{x}f(x)=x, the derivative is
f′(x)=12xf'(x)=\frac{1}{2\sqrt{x}}f′(x)=2x1
- More generally, for f(x)=g(x)f(x)=\sqrt{g(x)}f(x)=g(x), the derivative is
f′(x)=g′(x)2g(x)f'(x)=\frac{g'(x)}{2\sqrt{g(x)}}f′(x)=2g(x)g′(x)
(this comes from the chain rule: treat g(x)\sqrt{g(x)}g(x) as (g(x))1/2(g(x))^{1/2}(g(x))1/2 and apply the power rule).
