iCON Education - Differentiation BITSAT Test

Question 1: Palette 1/4

BITSAT 2024 MCQ

If $ x \sqrt{1+y}+y \sqrt{1+x}=0 $, then $ \frac{d y}{d x}= $

A

$ \frac{x+1}{x} $

B

$ \frac{1}{1+x} $

C

$ \frac{-1}{(1+x)^{2}} $

D

$ \frac{x}{1+x} $

Question 2: Palette 2/4

BITSAT 2021 MCQ

If $y = \sin \left( {2{{\tan }^{ - 1}}\sqrt {{{1 - x} \over {1 + x}}} } \right)$, then ${{dy} \over {dx}}$ is :

A

1

B

$-$1

C

${x \over {\sqrt {{x^2} - 1} }}$

D

${{ - x} \over {\sqrt {1 - {x^2}} }}$

Question 3: Palette 3/4

BITSAT 2020 MCQ

Let f(x) be a polynomial function of second degree. If f(1) = f($-$1) and a, b, c are in AP, then f'(a), f'(b) and f'(c) are in.

A

AP

B

GP

C

Arithmetic-Geometric progression

D

None of the above

Question 4: Palette 4/4

BITSAT 2020 MCQ

Given that $f(x) = 2{x^3} + {x^4} + \log x$ and assuming g to be the inverse function of f, compute the value of g'(3).

A

${1 \over 9}$

B

${1 \over 7}$

C

${1 \over 11}$

D

${1 \over 8}$