Differentiation by substitution - class-XI
| Description: differentiation by substitution | |
| Number of Questions: 31 | |
| Created by: Neema Pandya | |
| Tags: differentiation differential calculus i: fundamentals maths differencial calculus - differenciability and methods of differnciation |
Differentiate $\tan^{-1} \sqrt{\dfrac{1+\cos x}{1- \cos x}}$
If $y=\dfrac{1+x^2+x^4}{1+x+x^2}$ and $\dfrac{dy}{dx}=ax+b$, then the values of $a$ and $b$ are,
If $x=1(\theta+sin\,\theta), y=a(1-cos \theta)$, then at $\theta=\dfrac{\pi}{2},y'=\dfrac{2}{a}$.
If $f\left( x \right) =|x-2|,g\left( x \right) =f\left( f\left( x \right) \right) $, then for $x>4$, $g'(x)=$
Differential coefficient of $\log\ \sin x$ is :
If $f\left( x \right) =\sqrt { { x }^{ 2 }-2x+1 } $, then
The value of sin $ 2^o $ is approximately
Derivative of $(\sin x)^x + \sin^{-1} \sqrt{x}$ with respect to $x$ is
Let f(x) be a differentiable function satisfying $f(x+y)=f(x)+f(y)\forall x, y \in R$ and $f(0)=1$ then $\displaystyle\lim _{x\rightarrow 0}\dfrac{2^{f(\tan^2x)}-2^{f(\sin^2x)}}{x^3f(\sin x)}$ equals to?
If $t={ \sin { } }^{ -1 }{ 2 }^{ s }$ Then $\dfrac { ds }{ dt }$ is equal to
If $u=e^{x}(xcosy-ysiny)$ then $\frac{d^{2}y}{dx^{2}}+\frac{d^{2}u}{dy^{2}}=0$.
If $U=tan^{-1}(\dfrac{x^3+y^3}{x+y})$ , then $x\dfrac{du}{dx}+y\dfrac{du}{dy}=sinu$.
If $y=\sqrt{x}-\dfrac{1}{\sqrt{x}}$, then $2x\dfrac{dy}{dx}+y$=
If $x\sqrt {1+y}+y\sqrt {1+x}=0$ then $\dfrac {dy}{dx}=\dfrac {1}{(1+x)^{2}}$
Let $f(x)$ be a function continuous on $[1, 2]$ and differentiable on $(1, 2)$ satisfying $f(1)=2, f(2)=3$ and $f'(x)\ge 1\forall x\in (1, 2)$. Define $g(x)=\displaystyle \int _{1}^{x}{f(t)dt}\forall x\in [1, 2]$ then the greatest value of $g(x)$ on $[1, 2]$ is-
Given $y = x \sqrt{x^2+1}, \dfrac{dy}{dx}$=
If $\sin { { y+e }^{ -x\cos { y } } } =e\quad then\quad \frac { dy }{ dx } \quad at\quad (1,\pi )$ is equal to
If $\displaystyle \cos^{-1}\left ( \frac{x^{2}-y^{2}}{x^{2}+y^{2}} \right )=\log a$ then $\displaystyle \frac{dy}{dx}$ is equal to
If $\displaystyle y=\sec(\tan^{-1}x)$, then $\displaystyle \frac {dy}{dx}$ at $x=1$ is equal to
If $y=sec(tan^{-1}x)$, then $\displaystyle\frac{dy}{dx}$ is.
The differential equation $\dfrac {dy}{dx}=\dfrac {1}{ax+by+c}$ where a,b,c are all non zero real number ,is
If ${ x }^{ 2 }.{ e }^{ y }+2x{ ye }^{ x }+13=0$, then $\dfrac { dy }{ dx }$ is
Find: $\dfrac{d}{{\text dx}}\left( {\dfrac{{1 - \cos x}}{{\sin x}}} \right) \,\,\,$
Derivative of ${ \log { x } }^{ \cos { x } }$ with respect to $x$ is
If $xe^{xy}-y=\sin x$, then $\dfrac {dy}{dx}$ at $x=0$ is
$\dfrac {d}{dx}(x^{\ell n x})$ is equal to
If $y=(tan \, x)^{(tan\, x)^{tan\,x}}, $ then at $x=\dfrac{\pi}{4}, \dfrac{dy}{dx}$ is equal to
The solution of the differential equation, $y\,dx + \left( {x + {x^2}y} \right)dy = 0$ is
If $x=a\sin \theta$ and $y=b\cos\theta$, then $\displaystyle\frac{d^2y}{dx^2}$ is
The set of all points, where the function $f(x) = \sqrt {1 - e^{-x^{2}}}$ is differentiable, is
If $f(x) =x^{3} + e^{x/2}$ then $g"(1)$ is equal to, (where $f(x)$ and $g(x)$ are inverse functions of each other).