DERIVATIVE OF SEC SQUARE ROOT OF X

We know the derivative of secx, which is secxtanx.

(secx)' = secxtanx

We can find the derivative of sec(√x) using chain rule.

If y = sec(√x), find ᵈʸ⁄dₓ.

y = sec(√x)

Let u = √x.

Then, we have

y = secu

Now, y = secu and u = √x. That is, y is a function of u and u is a function of x.  

By chain rule, the derivative of y with respect to x,

Substitute y = secu and u = √x.

Substitute u = √x.

Therefore,

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