જો x^ 2/3 + y^ 2/3 = a^ 2/3 , તો dy dx = - Vidyadip

MCQ

જો ${x^{2/3}} + {y^{2/3}} = {a^{2/3}}$, તો ${{dy} \over {dx}} = $

A
${\left( {{y \over x}} \right)^{1/3}}$
✓
$ - {\left( {{y \over x}} \right)^{1/3}}$
C
${\left( {{x \over y}} \right)^{1/3}}$
D
$ - {\left( {{x \over y}} \right)^{1/3}}$

✓

Answer

Correct option: B.

$ - {\left( {{y \over x}} \right)^{1/3}}$

b
(b) ${x^{2/3}} + {y^{2/3}} = {a^{2/3}}$

==> $\frac{2}{3}{x^{ - 1/3}} + \frac{2}{3}{y^{ - 1/3}}\frac{{dy}}{{dx}} = 0$ or

$\frac{{dy}}{{dx}} = - {\left( {\frac{x}{y}} \right)^{ - 1/3}} = - {\left( {\frac{y}{x}} \right)^{1/3}}$.

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 5. continuity and differentiation→5. continuity and differentiation — all question types→ગણિત ધોરણ 12 સાયન્સ question papers→Gujarat Board ધોરણ 12 સાયન્સ question papers→Gujarat Board question paper generator→

Similar questions

Of the three independent events $E_1, E_2$ and $E_3$, the probability that only $E_1$ occurs is $\alpha$,only $E_2$ occurs is $\beta$ and only $E_3$ occurs is $\gamma$. Let the probability $p$ that none of events $E_1, E_2$ or $E_3$ occurs satisfy the equations ( $\alpha$ $-2 \beta) p=\alpha \beta$ and $(\beta-3 \gamma) p=2 \beta \gamma$. All the given probabilities are assumed to lie in the interval $(0,1)$.

Then $\frac{\text { Probability of occurrence of } E_1}{\text { Probability of occurrence of } E_3}=$

સંકલિત $\int_{0}^{\pi}|\sin 2 x| dx$ નું મૂલ્ય ......... છે.

$\mathop {\lim }\limits_{n \to \infty } \left[ {\frac{1}{n} + \frac{1}{{n + 1}} + \frac{1}{{n + 2}} + .....\frac{1}{{2n}}} \right] = $

જો $|U|=\begin{bmatrix}1 & 2 & 2 \\-2 & -1 & -1 \\ 1 & -4 & -3 \end{bmatrix}$ તો $U^{-1}$ ના બધા જ ઘટકોનો સરવાળો .......... થાય.

કિંમત શોધો : $\tan ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]$

વક્ર $x^2 = 4y$ અને રેખા $x = 4y - 2$ દ્વારા આવૃત પ્રદેશ નું ક્ષેત્રફળ મેળવો .

જો $y = y(x)$ એ વિકલ સમીકરણ $\frac{{dy}}{{dx}} + y\,\tan \,x = 2x\, + \,{x^2}\,\tan \,x\,,\,x\, \in \,\left( { - \frac{\pi }{2},\frac{\pi }{2}} \right),$ છે કે જેથી $y(0) = 1$ તો . . .. .

સીમિત શક્ય ઉકેલના પ્રદેશના શિરોબિંદુઓ $A(3,3), B(20,3),$ $\mathrm{C}(20,10), \mathrm{D}(18,12)$ અને $\mathrm{E}(12,12) $ છે. હેતુલક્ષી વિધેય $z=2 x+3 y$ ની ન્યૂનતમ કિંમત..

જો $f(x) = x^3-x^2+100\,x \, +1001\,;$ હોય તો

જો $x = 1$ હોય તો $y = 1,\;\frac{{dy}}{{dx}} = 0$ હોય તો વિકલ સમીકરણ $x\frac{{{d^2}y}}{{d{x^2}}} = 1$ નો ઉકેલ મેળવો.