CBSE Questions for Class 11 Commerce Applied Mathematics Differentiation Quiz 2 - MCQExams.com

If $$xy + x^2 y^2 = c$$; then the value of $$\displaystyle \frac{dy}{dx}$$ will be
  • $$\displaystyle \frac{x}{y}$$
  • $$\displaystyle \frac{-y}{x}$$
  • $$\displaystyle \frac{y}{x}$$
  • $$\displaystyle \frac{-x}{y}$$
If $${x}^{2}+{y}^{2}=4$$, then $$y\cfrac { dy }{ dx } +x$$ is equal to
  • $$4$$
  • $$0$$
  • $$1$$
  • $$-1$$
If $$y$$ is a function of $$x$$ and $$\log { \left( x+y \right)  } -2xy=0$$ then the value of $$y'(0)$$ is equal to
  • $$1$$
  • $$-1$$
  • $$2$$
  • $$0$$
Find the derivative of $$e^x+e^y=e^{x+y}$$
  • $$-e^{x-y}$$
  • $$e^{x-y}$$
  • $$-e^{y-x}$$
  • $$e^{y-x}$$
If $$y$$ is expressed in terms of a variable $$x$$ as $$y = f(x)$$, then $$y$$ is called
  • Explicit function
  • Implicit function
  • Linear function
  • Identity function
If $$y=\sqrt { \sin { x } +\sqrt { \sin { x } +\sqrt { \sin { x } +\dots \infty  }  }  } $$, then $$\left( 2y-1 \right) \dfrac { dy }{ dx } $$ is equal to
  • $$\sin { x } $$
  • $$-\cos { x } $$
  • $$\cos { x } $$
  • $$-\sin { x } $$
The value of $$\dfrac{d}{dx}\{x(x-1)(x-2)(x-3)\}$$ at $$x=3$$
  • $$0$$
  • $$3$$
  • $$6$$
  • $$24$$
Differentiate
 $$2x^{3/2} + 2x^{5/2} +C$$
  • $$\cfrac { dy }{ dx } =\sqrt { x } \left( 3+5x \right) $$
  • $$ \cfrac { dy }{ dx } =\sqrt { x } \left( 3-5x \right) $$
  • $$ \cfrac { dy }{ dx } =-\sqrt { x } \left( 3+5x \right) $$
  • None of these
Find $$\dfrac{dy}{dx}$$ of the given function  $$y^{x} =x^{y}.$$
  • $$y^x logy$$ = $$yx^{(y-1)}$$
  • $$0$$
  • $$x^ylogx$$
  • $$x^y logy$$ = $$yx^{(y-1)}$$
The derivative of $$y = \left( {1 - x} \right)\left( {2 - x} \right)...\left( {n - x} \right)\,at\,x = 1$$ is equal to :-
  • $$1$$
  • $$\left( { - 1} \right)\left( {n - 1} \right)!$$
  • $$n! - 1$$
  • $${\left( { - 1} \right)^{n - 1}}\left( {n - 1} \right)!$$
Find $$\dfrac{{dy}}{{dx}}$$ of the following $$y = 1 + 2x + 3{x^2} + \left( {n - 1} \right){x^{n - 2}}$$
  • $$x+2x^2+6x^3+(n-1)(n-2)x^{n-3}$$
  • $$2+6x+(n-1)x^{n-2}$$
  • $$2+6x+(n-1)(n-2)x^{n-3}$$
  • None
The value of $$\dfrac{d}{dx}\displaystyle\int\limits_{2}^{x^2}(t-1)dt$$
  • $$(x^2-1)$$
  • $$x(x^2-1)$$
  • $$2x(x^2-1)$$ 
  • none of these
Let $$f(x)=x^2e^x$$ then $$f''(0)=$$
  • $$1$$
  • $$0$$
  • $$2$$
  • $$7$$
The equation of the tangent to the curve $$y=x+\cfrac{4}{{x}^{2}}$$, that is parallel to the x-axis is
  • $$y=0$$
  • $$y=1$$
  • $$y=2$$
  • $$y=3$$
lf $$f(x)=\displaystyle \frac{x}{\sqrt{1-x^{2}}},g(x)=\frac{x}{\sqrt{1+x^{2}}}$$, then $$\displaystyle \frac{d}{dx}(fog (x))=$$
  • $$1$$
  • $$0$$
  • $$-1$$
  • $$2$$
Let $$y=\sqrt{(\sin x+\sin 2x+\sin 3x)^2+(\cos x+\cos 2x+\cos 3x)^2}$$ then which of  the following(s) is correct?
  • $$\dfrac{dy}{dx}$$ when $$x=\dfrac{\pi}{2}$$ is $$-2$$
  • Value of y when $$x=\dfrac{\pi}{5}$$ is $$\dfrac{3+\sqrt{5}}{2}$$
  • Value of y when $$x=\dfrac{\pi}{12}$$ is $$\dfrac{\sqrt{1}+\sqrt{2}+\sqrt{3}}{2}$$
  • y simplifies to $$(1+2\cos x)$$ in $$[0, \pi]$$
If $$\dfrac{d}{{dx}}\left( {\dfrac{{1 + {x^2} + {x^4}}}{{1 + x + {x^2}}}} \right) = ax + b,\,then\left( {a,b} \right) = $$
  • $$(-1,2)$$
  • $$(-2,1)$$
  • $$(2,-1)$$
  • $$(1,2)$$
If $$\sin ^{ 2 }{ mx } +\cos ^{ 2 }{ ny } ={ a }^{ 2 }$$ then $$\cfrac{dy}{dx}=$$
  • $$\cfrac{m.\sin{2mx}}{n.\sin{2ny}}$$
  • $$\cfrac{m.\sin{mx}}{n.\sin{nx}}$$
  • $$\cfrac{-m.\cos{2mx}}{n.\cos{2nx}}$$
  • $$\cfrac{n.\sin{2mx}}{m.\sin{2nx}}$$
Find $$\dfrac{dy}{dx}$$ of function $$y= e^{x^3} +\dfrac{1}{2} \log x $$
  • $$2.e^{x^3}x^2+\dfrac {1}{2x}$$
  • $$e^{x^3}x^2+\dfrac {1}{2x}$$
  • $$3.e^{x^3}x^2+\dfrac {1}{2x}$$
  • $$3.e^{x^3}x^2+\dfrac {1}{x}$$
$$x^{\frac{1}{2}} + 1=  t$$
differentiate w.r.t. x
  • $$\dfrac{dt}{dx} = \dfrac{1}{2\sqrt{x}}$$
  • $$\dfrac{dt}{dx} = \dfrac{1}{4\sqrt{x}}$$
  • $$\dfrac{dt}{dx} = \dfrac{1}{8\sqrt{x}}$$
  • $$\dfrac{dt}{dx} = \dfrac{1}{16\sqrt{x}}$$
Differentiate: $$x^{100} + \sin x - 1$$
  • $$100x^{99}-\cos x$$
  • $$100x^{99}+\cos x$$
  • $$x^{99}+\cos x$$
  • $$100x^{99}+\sin x$$
If $$f(x)=x\log x$$, then find f'(x).
  • $$1+x\log x$$
  • $$1+x$$
  • $$x+\log x $$
  • $$1+\log x$$
If $$\displaystyle\int \dfrac{f(x)dx}{\log(\sin x)}$$ $$=\log (\log(\sin x))$$ then $$f(x) =$$
  • $$sinx$$
  • $$cosx$$
  • $$\log(sinx)$$
  • $$cotx$$
if $$y=5x^2+8x$$ find $$\dfrac {dy}{dx}$$
  • $$10x+8$$
  • $$5x+8$$
  • $$10x^2+8x$$
  • none of these
If $$y=\log \sin x$$ find $$x$$ if $$y=0$$
  • $$\dfrac {\pi}2$$
  • $$\pi $$
  • $${\dfrac {\pi}3}$$
  • $$\dfrac {-\pi}2$$
lf $$ \mathrm{f}(\mathrm{x})=0$$ has a repeated root $$ \alpha$$, then another equation having $$\alpha$$ as root, is 
  • $$\mathrm{f}(2\mathrm{x})=0$$
  • $$\mathrm{f}(3\mathrm{x})=0$$
  • $$\mathrm{f}^{'}(\mathrm{x})=0$$
  • $$\mathrm{f}^{''}(\mathrm{x})=0$$

lf $$[\mathrm{x}]$$ denotes the greatest integer contained in $$\mathrm{x},$$ then for 4 $$<\mathrm{x}<5,\ \displaystyle \frac{d}{dx}\{[x]\}=$$
  • $$[x - 4, 5]$$
  • $$[x]$$
  • $$0$$
  • $$1$$
lf $$y=\log{(x+\sqrt{1+x^2})}$$, then $$y^{''}(0)$$ is
  • $$0$$
  • $$1$$
  • $$-1$$
  • $$2$$

$$\displaystyle \mathrm{A}:\dfrac{d}{dx}(\sin x)\ at\ x=\frac{\pi}{2}$$

$$\displaystyle \mathrm{B}:\dfrac{d}{dx}(\tan^{-1}{x})$$ at $$ {x}=1$$

$$\displaystyle \mathrm{C}:\dfrac{d}{dx}(\mathrm{e}^{x})$$ at $${x}=0$$

$$\mathrm{D}:\dfrac{d}{dx}(x^{x})\ at\ x=e$$

Arrangement of the above values in the increasing order of the magnitude
  • B, C, A, D
  • D, A, B, C
  • D, B, C, A
  • A, B, C, D
lf $$y=\displaystyle \log{\left(\frac{1+x}{1-x}\right)^{\frac{1}{4}}}-\frac{1}{2}\tan^{-1}(x)$$, then $$\displaystyle \frac{dy}{dx}=$$
  • $$\displaystyle \frac{x}{1-x^{2}}$$
  • $$\displaystyle \frac{x^{2}}{1-x^{4}}$$
  • $$\displaystyle \frac{x}{1+x^{4}}$$
  • $$\displaystyle \frac{x}{1-x^{4}}$$
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