Find the derivative of the function.

Question

s(x)=x+7/x

s^1(x)=

Answer 1

Probably easier to differentiate after first rewriting the function as a fraction the radical:

s(x) = √((x+7)/(x)) and, further simplifying, s(x) = (1 + x^-1)^1/2

We need to apply chain rule: ds/dx = - 1/x²·(1/2)·(1 + x^-1)^-1/2 or -1/(2x²√(1 + x^-1))

Answer 2

s'(x) = d/dx (√x ) + d/dx (7/√x)

= d/dx(x^1/2) + d/dx ( 7 x^-1/2)

= 1/2 x^-1/2 - 7/2 x^-3/2