Question

How do you find the derivative of `cos[sqrt (x)]`?

Answer 1

Use the chain rule.

Explanation:

`d/dx(sqrtx) =d/dx(x^(1/2)) =1/2x^(1/2-1)=1/2x^(1/2-2/2)=1/2x^(-1/2)=1/(2x^(1/2))= 1/(2sqrtx)`

`d/dx(cos(sqrtx)) = -sin(sqrtx) d/dx(sqrtx)`

`= -sin(sqrtx) (1/(2sqrtx))`