The derivative of f tan x with respect to g x at x- 4- where f-1-2- g- 2 -4 is

The correct option is A 1 √( 2 ) df(tanx)dg(secx) = df(tanx)/dxdg(secx)/dx =f'(tanx) × sec^2xg'(secx) × secx tanx =2 ×√(2)^24 ×√(2)× 1 # ...

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Derivative of Standard Functions

The derivativ...

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The derivative of $f (tan x)$ with respect to $g (sec x)$ at $x = \frac{π}{4}$ , where $f^{'} (1) = 2; g^{'} (\sqrt{2}) = 4$ is

\frac{1}{\sqrt{2}}

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\sqrt{2}

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f (tan x)

g (sec x)

x = \frac{π}{4},

f^{'} (1) = 2

g^{'} (\sqrt{2}) = 4,

(\sqrt{2})

\frac{π}{4}

g (x) = f (tan x) + f (cot x)

x \in (\frac{π}{2}, π)

f^{''} (x) < 0 \forall x \in (\frac{π}{2}, π),

u = f (cot x)

v = g (cosec x)

f^{'} (1) = \sqrt{2}

g^{'} (\sqrt{2}) = 2

{(\frac{d u}{d v})}_{x = \frac{π}{4}} = 1

u = f (x), v = g (x)

f

g

\frac{d u}{d v} = \frac{d u / d x}{d v / d x}

n ϵ N

f (x) = m i n {1 - {tan}^{n} x, 1 - {sin}^{n} x, 1 - x^{n}}

x ϵ (- \frac{π}{2}, \frac{π}{2})

f

x = \frac{π}{4}

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