derive the square root of x squared minus 5

Question

 

g(x) = √2xsquared − 5

find the derivative of the above with special reference to the root.

Note that the above root is over the whole 2xsquared-5 and not just the 2xsquared.

Answer 1

g(x) = √2xsquared − 5  find the derivative of the above with special reference to the root.

 

Note that the above root is over the whole 2xsquared-5 and not just the 2xsquared.

In that case, you should write: g(x) = √(2x^2 − 5)

 

What we have is: g = √u, where u = 2x^2 - 5. Then

dg/dx = (dg/du).(du/dx)

dg/dx = (1/(2√u)).(4x)

dg/dx = 2x/√(2x^2 - 5)