COMPASSLearning

Talk to us Register Login

JEE Main · 2024 · 06 Apr 2024 · Shift 2 · Differentiation

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

(A)5
(B)3
(C)8
(D)4✓ Correct

Answer: (D)

Solution

g (x) = h (e^{x}) e^{h (x)}

, so

g^{'} (x) = h^{'} (e^{x}) e^{x} e^{h (x)} + h (e^{x}) e^{h (x)} h^{'} (x)

. At

x = 0

:

g^{'} (0) = h^{'} (1) \cdot 1 \cdot e^{h (0)} + h (1) e^{h (0)} h^{'} (0) = h^{'} (1) + h (1) h^{'} (0) = 2 + 1 \cdot 2 = 4

(using

h (0) = 0, h (1) = 1, h^{'} (0) = h^{'} (1) = 2

).

JEE Main · 2024 · 06 Apr 2024 · Shift 2 · 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 →
Let $f (x) = ax^{3} + bx^{2} + cx + 41$ be such that
$f (1) = 40, f^{'} (1) = 2$ and $f^{''} (1) = 4$ .
Then $a^{2} + b^{2} + c^{2}$ is equal to :
JEE Main 2024View solution →