Mathematics · 2023
JEE Main · 6 April 2023, Shift 1 · Q9
If 2 x^y+3 y^x=20, then (d y)/(d x) at (2,2) is equal to:
If $\displaystyle 2 x^y+3 y^x=20$, then $\displaystyle \frac{d y}{d x}$ at $\displaystyle (2,2)$ is equal to:
Official answer
From NTA’s final answer key for this paper.
(4)
$\displaystyle -\left(\frac{2+\log _e 8}{3+\log _e 4}\right)$
More from Methods of Differentiation
- If y(x)=x^x, x>0, then y^′ ′(2)-2 y^′(2) is equal to:2023
- Let f: R → R be a differentiable function that satisfies the relation f(x+y)=f(x)+f(y)-1, ∀ x, y ∈ R. If f^′(0)=2, then |f(-2)| is equal to ____.2023
- Suppose for a differentiable 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:2024
- If f(x)=x^3-x^2 f^′(1)+x f^′ ′(2)-f^′ ′ ′(3), x ∈ R, then2023
- 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 to:2023
- Let f(x)=x^3+x^2 f^′(1)+x f^′ ′(2)+f^′ ′ ′(3), x ∈ R. Then f^′(10) is equal to ____.2024
- Suppose f(x)=((2^x+2^-x) tan x √(tan^-1(x^2-x+1)))/((7 x^2+3 x+1)^3). Then the value of f^′(0) is equal to2024
- Let f be a real polynomial of degree n such that f(x)=f^′(x) f^′ ′(x), for all x ∈ R. If f(0)=0, then 36(f^′(2)+f^′ ′(2)+∫_0^2 f(x) d x) is equal to:2026
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.