If the derivative of $ f(\tan x) $ w.r.t. $ g(\sec x) $ at $ x=\frac{\pi}{4} $, where $ f^{\prime}(1)=2 $ and $ g^{\prime}(\sqrt{2})=4 $ is $ \frac{\sqrt{2}}{k} $ then find $ k $ ?

Question

If the derivative of $ f(\tan x) $ w.r.t. $ g(\sec x) $ at $ x=\frac{\pi}{4} $, where $ f^{\prime}(1)=2 $ and $ g^{\prime}(\sqrt{2})=4 $ is $ \frac{\sqrt{2}}{k} $ then find $ k $ ?,

MARKS App · Accepted Answer

Let u = f tan x and v = g sec x ⇒ d u d x = f ' tan x sec 2 x and d v d x = g ' sec x sec x tan x ⇒ d u d v = d u d x / d v d x = f ' tan x sec 2 x g ' sec x sec x tan x ⇒ d u d v x = π 4 = f ' tan π 4 g ' sec π 4 sin π 4 = f ' 1 2 g ' 2 = 2 2 4 = 1 2 = 1 2 × 2 2 = 2 2 = 2 k ⇒ k = 2 .

Search any question & find its solution

Looking for more such questions to practice?