New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differentiation question

2023 · 6 Apr · Shift 1 · Q35

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Differentiation
2023 · 6 Apr · Shift 1 · Q35

Differentiation question

2023 · 6 Apr · Shift 1 · Q35

JEE MainMathematicsDifferentiationMCQ+4 / −1

If

2 x^{y}+3 y^{x}=20

, then

\frac{d y}{d x}

at

(2,2)

is equal to :

A
$-\left(\frac{3+\log _{e} 16}{4+\log _{e} 8}\right)$
B
$-\left(\frac{2+\log _{e} 8}{3+\log _{e} 4}\right)$
C
$-\left(\frac{3+\log _{e} 8}{2+\log _{e} 4}\right)$
D
$-\left(\frac{3+\log _{e} 4}{2+\log _{e} 8}\right)$

More from Differentiation

Let $f (x) = \frac{s i n x + c o s x - 2}{s i n x - c o s x}, x \in [0, π] - {\frac{π}{4}}$ . Then $f (\frac{7 π}{12}) f^{''} (\frac{7 π}{12})$ is equal to2023 · MCQ
For the differentiable function $f : R - {0} \to R$ , let $3 f (x) + 2 f (\frac{1}{x}) = \frac{1}{x} - 10$ , then $f (3) + f^{'} (\frac{1}{4})$ is equal to2023 · MCQ
Let $f (x) = \sum_{k = 1}^{10} k x^{k}, x \in R$ . If $2 f (2) + f^{'} (2) = 119 (2)^{n} + 1$ then $n$ is equal to 2023 · Numerical
If $f (x) = x^{3} - x^{2} f^{'} (1) + x f^{''} (2) - f^{'''} (3), x \in R$ , then2023 · MCQ
Let $y (x) = (1 + x) (1 + x^{2}) (1 + x^{4}) (1 + x^{8}) (1 + x^{16})$ . Then $y^{'} - y^{''}$ at $x = - 1$ is equal to2023 · MCQ
Let $f : R \to R$ be a differentiable function that satisfies the relation $f (x + y) = f (x) + f (y) - 1, \forall x, y \in R$ . If $f^{'} (0) = 2$ , then $∣ f (- 2) ∣$ is equal to .2023 · Numerical
Let $f$ and $g$ be the twice differentiable functions on $R$ such that $f^{''} (x) = g^{''} (x) + 6 x f^{'} (1) = 4 g^{'} (1) - 3 = 9 f (2) = 3 g (2) = 12$ . Then which of the following is NOT true?2023 · MCQ
Let $f^{1} (x) = \frac{3 x + 2}{2 x + 3}, x \in R - {\frac{- 3}{2}}$ For $n \geq 2$ , define $f^{n} (x) = f^{1} o f^{n - 1} (x)$ . If $f^{5} (x) = \frac{a x + b}{b x + a}, gcd (a, b) = 1$ …2023 · Numerical