જો e^ x +e^ y =e^ x-y તો d y d x = ..................... - Vidyadip

MCQ

જો $e^{x}+e^{y}=e^{x-y}$ તો $\frac{d y}{d x}=$ .....................

A
$e^{x-y}$
B
$e^{y-x}$
✓
$-e^{y-x}$
D
$-e^{x-y}$

✓

Answer

Correct option: C.

(C) $-e^{1-x}$
$\begin{array}{ll} & \\ & e^x+e^y=e^{x+y} \\ \therefore \quad & e^x+e^y=e^x \cdot e^y \\ \therefore & e^{-y}+e^{-x}=1\end{array}$
$\therefore \quad e^{-y}\left(-\frac{d y}{d x}\right)+e^{-x}(-1)=0$
$\begin{array}{l}\therefore \quad-e^{-y} \frac{d y}{d x}=e^{-x} \\ \therefore \quad \frac{d y}{d x}=-e^{y-r}\end{array}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Model Paper 1→Model Paper 1 — all question types→ગણિત ધોરણ 12 સાયન્સ question papers→Gujarat Board ધોરણ 12 સાયન્સ question papers→Gujarat Board question paper generator→

Similar questions

જો $\frac{d y}{d x}+\frac{2^{x-y}\left(2^{y}-1\right)}{2^{x}-1}=0, x, y>0, y(1)=1$, તો $y (2)=\dots\dots\dots$

$\left| {\,\begin{array}{*{20}{c}}{a - b - c}&{2a}&{2a}\\{2b}&{b - c - a}&{2b}\\{2c}&{2c}&{c - a - b}\end{array}\,} \right| = $

A bag ‘$A$’ contains $2$ white and $3$ red balls and bag ‘$B$’ contains $4$ white and $5$ red balls. One ball is drawn at random from a randomly chosen bag and is found to be red. The probability that it was drawn from bag $‘B’$ was

પરવલયો કે જેની અક્ષ $x-$ અક્ષ છે. તેવા વક્રોના વિકલ સમીકરણની ક્ક્ષા $ +$ પરિમાણની સંખ્યા $......$ છે.

$\overrightarrow a,\overrightarrow b$અને $\overrightarrow c$ વિષમતલીય સદિશો છે અને $\lambda$ કોઈક વાસ્તવિક સંખ્યા હોય , તો $\left[\lambda\left(\overrightarrow{a}+\overrightarrow{b}\right) \ \ \lambda^{2}\overrightarrow{b} \ \ \lambda\overrightarrow{c}\right] =\left[\overrightarrow{a} \ \overrightarrow{b} \ \ +\overrightarrow{c} \ \overrightarrow{b}\right]$ એ $...........$

$f(x) = 3|2 + x|$ નું ${x_0} = - 3$ આગળ વિકલન મેળવો.

બિંદુ $(0,1,-1)$ થી $2\sqrt{14}$ અંતરે આવેલું રેખા $ \ x=\frac{y-1}{2}= \frac{z+1}{-3}$ ૫૨નું બિંદુ $........$ છે.

$\int_{}^{} {\cos x\sqrt {4 - {{\sin }^2}x} } \;dx = $

જો $A = \left[ {\begin{array}{*{20}{c}}3&{ - 5}\\{ - 4}&2\end{array}} \right],$ તો ${A^2} - 5A = $

$\int_{\pi /6}^{\pi /3} {{{\sec }^{2/3}}\,x\,\,\cos e{c^{4/3}}\,x\,dx} $ મેળવો.