If yx-xy=1, then the value of (d y/d x) at x=1 is equal to

Question

If yx-xy=1, then the value of (d y/d x) at x=1 is equal to (A) 2(1- ln 2) (B) 2+ ln 2 (C) 2(1+ ln 2) (D) 2- ln 2

Tardigrade Admin · Accepted Answer

P( x =1, y =2) e x ln y - e y ln x =1 ∴ On differentiating with respect to x, we get ⇒ yx((x/y) ⋅ y prime+ ln y)-xy((y/x)+y prime ⋅ ln x)=.0 ⇒ (d y/d x)|(x=1, y=2)=2(1- ln 2)

Q. If $y^{x} - x^{y} = 1$ , then the value of $\frac{d y}{d x}$ at $x = 1$ is equal to

$2 (1 - ln 2)$

$2 + ln 2$

$2 (1 + ln 2)$

$2 - ln 2$

$P (x = 1, y = 2)$
$e^{x l n y} - e^{y l n x} = 1$
$∴$ On differentiating with respect to $x$ , we get
$\Rightarrow y^{x} (\frac{x}{y} \cdot y^{'} + ln y) - x^{y} (\frac{y}{x} + y^{'} \cdot ln x) = 0 \Rightarrow \frac{d y}{d x} ∣ ∣_{(x = 1, y = 2)} = 2 (1 - ln 2)$

Q. If yx−xy=1, then the value of dxdy​ at x=1 is equal to

2(1−ln2)

2+ln2

2(1+ln2)

2−ln2