Question

If y= sec( tan x) , than dy/ dx at x = 1 is equal to​

Answer 1

Answer:

y=sec(tan

−1

x)

dx

dy

=sec(tan

−1

x)tan(tan

−1

x)⋅

1+x

2

1

dx

dy

∣

x=1

=

2

×1×

2

1

=

2

1

.

Answer 2

${\boxed{\huge{\red{A}{\green{N}{S}{\orange{W}{\pink{E}{\purple{R}}}}}}}}$

$y = sec( {tan}^{ - 1} x)$

$\frac{dy}{dx} = sec( {tan}^{ - 1} x)tan( {tan}^{ - 1} x). \frac{1}{1 + {x}^{2} }$

$\frac{dy}{dx} |x = 1 = \sqrt{2} \times 1 \times \frac{1}{2} = \frac{1}{ \sqrt{2} }$

$∴ \frac{dy}{dx} = \frac{1}{ \sqrt{2} }$

$\underbrace\red{hope \: it \: helps \: u \: mate}$