NDA 2025 Maths · Mathematics · Derivatives · medium

The slope of the tangent to the curve y=ln (tan x) at the point where x=(π)/(4) is

Single correct option

The slope of the tangent to the curve

y=\ln(\tan x)

at the point where

x=\dfrac\pi4

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Answer: (D) $2$

y'=\frac{\sec^2x}{\tan x}=\frac{1}{\sin x\cos x}=\frac{2}{\sin2x}

. At

x=\frac\pi4

\sin\frac\pi2=1

, so

y'=2

. The value

1

is the value of

\tan\frac\pi4

\frac12

comes from inverting, and

\sqrt2

\sec\frac\pi4

left unsimplified.

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