d/dx of root x

d/dx of root x

 

\(\frac{d}{dx}\;x^{0.5} = 0.5x^{-0.5} = \frac{1}{2\sqrt{x}}\)

 

 

d/dx of 1/rootx

 

\(\frac{d}{dx}\frac{1}{\sqrt{x}}\;\\\\ =\;\frac{d}{dx}\;x^{-0.5}\\\\ =-0.5x^{-1.5}\\\\ =\frac{-1}{2x\sqrt{x}}\)

 

 

d/dx of y

 

\(\frac{d}{dx}\;y=1\frac{dy}{dx}=\frac{dy}{dx}\)

 

 

 

d/dx of e power x

 

\(\frac{d}{dx}\;e^x\;=e^x\)

d/dx(sqrt(x)) = 1/(2 sqrt(x))

d/dx(1/sqrt(x)) = -1/(2 x^(3/2))

d/dx(y(x)) = y'(x)

d/dx(e^x) = e^x