Question

find dy/dx of y=sec sqrtx

Answer 1

\[\large y = sec(\sqrt{x})\]

Like that?

Answer 2

yeah

Answer 3

Okay sorry about that wait, was helping others as well :)

So we just need to utilize the chain rule here

\[\large \frac{dy}{dx} sec(x^{1/2})\]

If we let u = x^(1/2)

\[\large \frac{dy}{dx}sec(u) = \frac{dy}{dx} sec(u) \frac{dy}{dx}u\]

So the derivative of \(\large sec(u) = sec(u)tan(u)\)
and the derivative of u which is x^(1/2) = 1/2(x)^(-1/2)

So altogether we have *remember to change u back to x^(1/2)

\[\large \frac{dy}{dx} sec(\sqrt{x}) = \frac{sec(\sqrt{x})tan(\sqrt{x})}{2\sqrt{x}}\]

Answer 4

thank you!!