Question

The derivative of sec (tan√x).
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Answer 1

Answer:

[sec ( tan (√x)) . tan ( tan (√x))] × [$sec^{2} \sqrt{x}$] × [1 / 2√x]

Step-by-step explanation:

y = sec ( tan (√x))

then derivative of y w.r.t x is :

We know the derivative of sec x = sec x . tan x

So,  [sec ( tan (√x)) . tan ( tan (√x))] × [derivative of (tan (√x))]

We know derivative of tanx = $sec^{2} x$

⇒  [sec ( tan (√x)) . tan ( tan (√x))] × [$sec^{2} \sqrt{x}$] × [derivative of √x]

We know derivative of √x = 1 / 2√x

⇒ [sec ( tan (√x)) . tan ( tan (√x))] × [$sec^{2} \sqrt{x}$] × [1 / 2√x]

∴ Derivative of the given expression is :

[sec ( tan (√x)) . tan ( tan (√x))] × [$sec^{2} \sqrt{x}$] × [1 / 2√x]