Question

y = `sec (tan sqrt(x))`

पर्याय

• `sec^2 sqrt(x)`

• `1/(2sqrt(x)) sec sqrt(x)`

• `tan sqrt(x)`

• None of these

Answer 1

None of these

Explanation:

Let `y = sec (tan sqrt(x))`

Put `sqrt(x) = t, S = tan t`

⇒ `y = sec s, s = tan t, t = sqrt(x)`

Now, `(dy)/(dx) = (dy)/(dx) xx (ds)/(st) xx (dt)/(dx)` ......(1)

`y = secs, (dy)/(ds) = secs tan s`.

`s = tan t, (ds)/(dt) = sec^2t`.

`t = sqrt(x) * (dt)/(dx) = 1/(2sqrt(x))`

Putting, there value in (1)

`(dy)/(dx) (sec s tan s) (sec^2t) (1/(2sqrt(x)))`

= `sec (tan t) tan (tan t). sec^2 sqrt(x) * 1/(2sqrt(x))`

= `1/(2sqrt(x)) sec tan (sqrt(x)) tan`

`(tan (sqrt(x))) sec^2 sqrt(x)`