COMPASSLearning

Talk to us Register Login

JEE Main · 2013 · 07 Apr 2013 · Offline · Differentiation

If

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

, then

\frac{d y}{d x}

at

x = 1

is equal to

(A) $\frac{1}{2}$
(B)1
(C) $2$
(D) $\frac{1}{2}$ ✓ Correct

Answer: (D)

Solution

Let

θ = tan^{- 1} x

, so

tan θ = x

and

sec θ = 1 + x^{2}

, which means

y = sec (tan^{- 1} x) = 1 + x^{2}

. Differentiating,

\frac{d y}{d x} = \frac{x}{1 + x ^{2}}

, and at

x = 1

this is

\frac{1}{2}

.

JEE Main · 2013 · 07 Apr 2013 · Offline · Single correct option

Practise more: all JEE Main PYQs on Differentiation →

More JEE Main questions on Differentiation

Let $f (x) = x^{3} + x^{2} f^{'} (1) + 2 x f^{''} (2) + f^{'''} (3)$ , $x \in R$ . Then the value of $f^{'} (5)$ is :
JEE Main 2026View solution →
If $y (x) = sin x 271 cos x 281 sin x + cos x + 1 271$ , $x \in R$ , then $\frac{d ^{2} y}{d x ^{2}} + y$ is equal to
JEE Main 2025View solution →
Let $f (x) = x^{5} + 2 e^{x /4}$ for all $x \in R$ . Consider a function $g (x)$ such that $(g \circ f) (x) = x$ for all $x \in R$ . Then the value of $8 g^{'} (2)$ is
JEE Main 2024View solution →
Let $f (x) = x^{5} + 2 x^{3} + 3 x + 1, x \in R$ , and $g (x)$ be a function such that $f (g (x)) = x$ for all $x \in R$ . Then $\frac{g ( 7 )}{g ^{'} ( 7 )}$ is equal to:
JEE Main 2024View solution →
If $y (θ) = \frac{2 c o s θ + c o s 2 θ}{c o s 3 θ + 4 c o s 2 θ + 5 c o s θ + 2}$ , then at $θ = \frac{π}{2}$ , $y^{''} + y^{'} + y$ is equal to
JEE Main 2024View solution →
Suppose for a function $h, h (0) = 0, h (1) = 1$ and $h^{'} (0) = h^{'} (1) = 2$ . If $g (x) = h (e^{x}) e^{h (x)}$ , then $g^{'} (0)$ is equal to
JEE Main 2024View solution →