JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

y=\tan ^{-1}\left[\frac{\sin x+\cos x}{\cos x-\sin x}\right]

, then

d y / d x=

View answer and explanation

Correct option: D

Option D (1) is correct because simplifying the expression inside the arctangent yields

\tan(\frac{{\pi}}{{4}} + x)

, so

y = \frac{{\pi}}{{4}} + x

, and

\frac{{dy}}{{dx}} = 1

More Questions from DIFFERENTIATION

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x

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x y=1

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[x]

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x=k, k

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y = {\sec ^{ - 1}}\left[ {\mathrm{cosec}x} \right] + \mathrm{cose}{\mathrm{c}^{ - 1}}\left[ {\sec x} \right] + {\sin ^{ - 1}}[\cos x] + {\cos ^{ - 1}}[\sin x],

\frac{{dy}}{{dx}}

\frac{d}{d x} \sin ^{-1}\left(3 x-4 x^{3}\right)

z = y + f\left( v \right),

v = \left( {\frac{x}{y}} \right),

v\frac{{\partial z}}{{\partial x}} + \frac{{\partial z}}{{\partial y}}