Implicit Differentiation

Q. If $2^x+2^y=2^{x+y}$ then the value of $\frac{dy}{dx}atx=y=1is$

1. 0
2. - 1
3. 1
4. 2

Q. If $y=\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y+....\infty ,}}}}$ then $\frac{dy}{dx}$ is equal to

1. None of these
2. $\frac{y^2-x}{2y^3-2xy-1}$
3. $\frac{1}{2y-1}$
4. $(2y-1)$

Q. $Ify=\sqrt{sinx+\sqrt{sinx+\sqrt{sinx+.....\infty }}},then\frac{dy}{dx}isequalto$

1. $\frac{2x-1}{cosx}$
2. $\frac{2y-1}{cosx}$
3. $\frac{cosx}{2y-1}$
4. $\frac{cosx}{2x-1}$

Q. $If{x}^2+y^2=t-\frac{1}{t}and{x}^4+y^4=t^2+\frac{1}{t^2},then{x}^{3}y\frac{dy}{dx}equals$

1. - 1
2. 0
3. 1
4. None of these

Q. If sin y = x sin (a + y) and $\frac{dy}{dx}=\frac{A}{1+x^2-2xcos{a}^{\prime }},$ then the value of A is

1. 2
2. cos a
3. sin a
4. None of these

Q. $Ifsin(x+y)=lo{g}_e(x+y),then\frac{dy}{dx}isequalto$

1. - 2
2. 2
3. 1
4. - 1

Q.

For the curve represented implicitly as $3^x-2^y=1$, the value of $\underset{x\to \infty }{lim}\left(\frac{dy}{dx}\right)$ is

1. equal to 0

2. non existent

3. equal to 1

4. equal to $lo{g}_{2}3$

Q.

Let $y$ be an implicit function of $x$ defined by $x^{2x}-2x^{x}coty-1=0.$ Then $y^{\prime }\left(1\right)$ equals

1. log 2

2. - 1

3. - log 2

4. 1

Q. The value of $y^{\prime \prime }\left(1\right)$ if $x^3-2x^2{y}^2+5x+y-5=0$ when $y\left(1\right)=1$, is equal to

1. $8$
2. $\frac{22}{7}$
3. $-7\frac{21}{28}$
4. $-8\frac{22}{27}$

Q. If $2^x+2^y=2^{x+y}$, then $\frac{dy}{dx}$ is equal to

1. $2^{x-y}.\frac{2^y-1}{1-2^x}$
2. $\frac{(2^x+2^y)}{(2^x-2^y)}$
3. $\frac{2^{x+y}-2^x}{2^y}$
4. $\frac{(2^x+2^y)}{(1+2^{x+y})}$