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Recent questions tagged differentiability

If $e^{x+y}=xy,$ what is $\large\frac{dy}{dx}$?

asked Jan 29, 2014 by balaji

1 answer

The set of points where the function $f(x)=\sqrt{1-e^{-x^2}}$ is differentiable is

asked Jan 6, 2014 by sreemathi.v

1 answer

The set of all points where the function $f(x)=\large\frac{x}{(1+|x|)}$ is differentiable is

asked Jan 4, 2014 by sreemathi.v

1 answer

Let $[x]$ denote the greatest integer less than or equal to x. If $f(x)=[x\sin\pi x]$, then $f(x)$ is

asked Jan 3, 2014 by sreemathi.v

1 answer

If $f(x)=x(\sqrt{x}-\sqrt{x+1})$ then

asked Jan 3, 2014 by sreemathi.v

1 answer

If $x+|y|=2y$, then $y$ as a function of x is

asked Jan 3, 2014 by sreemathi.v

1 answer

The function $f(x)$ = $(x^2-1)\;$ $|x^2-3x+2|$ + $\cos(|x|)$ is not differentiable at

asked Jan 3, 2014 by sreemathi.v

1 answer

The function given by $y=||x|-1|$ is differentiable for all real numbers except the points

asked Jan 3, 2014 by sreemathi.v

1 answer

If $f$ is twice differentiable and $f''(0)=2$ then $\lim\limits_{x\to 0}\large\frac{2f(x)-3f(2x)+f(4x)}{x^2}$=

asked Jan 2, 2014 by sreemathi.v

1 answer

Let $f:R\rightarrow R$ be a function such that $f(x+y)=f(x)+f(y)\forall x,y\in R$ if $f(x)$ is differentiable at $x=0$ then

asked Dec 31, 2013 by sreemathi.v

1 answer

Let $f:R\rightarrow R$ be a function defined by $f(x)=min\{x+1,\mid x\mid+1\}$. Then which of the following is true ?

asked Dec 31, 2013 by sreemathi.v

1 answer

If $f$ is a real valued differentiable function satisfying $\mid f(x)-f(y)\mid\leq (x-y)^2,x,y\in R$ and $f(0)=0$ then $f(1)$ equals

asked Dec 31, 2013 by sreemathi.v

1 answer

$f(x)$ and $g(x)$ are two differentiable function on [0,2] such that $f''(x)-g''(x)=0$. $f'(1)=2g'(1)=4f(2)=3g(2)=9$ then $f(x)-g(x)$ at $x=\large\frac{3}{2}$ is

asked Dec 31, 2013 by sreemathi.v

1 answer

If $f(x)$ is continuous and differentiable function and $f(1/n)=0\forall n \geq 1$ and $n\in 1$ then

asked Dec 31, 2013 by sreemathi.v

1 answer

Let $f:R\rightarrow R$ be a differentiable function and $f(1)=4$, then the value of $\large \int_4^{f(x)}\large\frac{2t\;dt}{x-1}$ is

asked Dec 31, 2013 by sreemathi.v

1 answer

For a real number y, let [y] denotes the greatest integer less than or equal to y. Then the function $f(x)=\large\frac{\tan(\pi[x-\pi])}{1+[x]^2}$ is

asked Dec 31, 2013 by sreemathi.v

1 answer

$\lim\limits_{h\to 0}\large\frac{f(2h+2+h^2)-f(2)}{f(h-h^2+1)-f(1)}$ given that $f'(2)=6$ and $f'(1)=4$

asked Dec 30, 2013 by sreemathi.v

1 answer

Let $f:R\to R$ be such that $f(1)=3$ and $f'(1)=6$.Then $\lim\limits_{x\to 0}\bigg[\large\frac{f(1+x)}{f(1)}\bigg]^{1/x}$ equals

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 1}\large\frac{\sqrt{1-\cos 2(x-1)}}{x-1}$=

asked Dec 30, 2013 by sreemathi.v

1 answer

Let $f:R\rightarrow R$ be a differentiable function having $f(2)=6,f'(2)=\large\frac{1}{48}$.Then $\lim\limits_{x\to 2}\int_6^{f(x)}\large\frac{4t^3dt}{x-2}$ equals

asked Dec 24, 2013 by sreemathi.v

1 answer

The function $f(x)=\left\{\begin{array}{1 1}1&x\leq -1\\|x|&-1< x < 1\\0&x\geq 1\end{array}\right.$

asked Dec 24, 2013 by sreemathi.v

1 answer

Value of $\lim_{x\to 2^-}\{x+(x-[x]^2)\}$ is

asked Dec 24, 2013 by sreemathi.v

1 answer

If $f(x)=\mid x-25\mid$ and $g(x)=f(f(x))$,find $g'(x)$ for $x > 50$

asked Dec 23, 2013 by sreemathi.v

1 answer

If function $f(x)$ is differentiable at $x=a$ then $\lim\limits_{x\to a}\large\frac{x^2f(a)-a^2f(x)}{x-a}$ is

asked Dec 23, 2013 by sreemathi.v

1 answer

If $( x = \sqrt {a^{\large sin^{-1}t}}, \: y = \sqrt {a^{\large cos^{-1}t}} ),$ what is the value of $\frac {\large dy}{\large dx}$

asked Dec 22, 2013 by balaji.thirumalai

1 answer

If $x^y\; y^x = 100$, evaluate $\large \frac{dy}{dx}$

asked Dec 22, 2013 by balaji.thirumalai

1 answer

If $(x)$ is differentiable and strictly increasing function then the value of $\lim\limits_{x\to 0}\large\frac{f(x^2)-f(x)}{f(x)-f(0)}$ is

asked Dec 20, 2013 by sreemathi.v

1 answer

Let $f:R\rightarrow R$ be a function defined by $f(x)=max(x,x^3)$.The set of all points where $f(x)$ is not differentiable

asked Dec 20, 2013 by sreemathi.v

1 answer

Let $f(x)=x|x|$. The set of points where $f(x)$ is twice differentiable is

asked Dec 20, 2013 by sreemathi.v

1 answer

Let $f(x)=\left\{\small\begin{array}{1 1}(x-1)^2\sin\large\frac{1}{(x-1)}-\normalsize |x|&ifx\neq 1\\-1&if\;x=1\end{array}\right.$ be a real valued function. Then the set of points where $f(x)$ is not differentiable is

asked Dec 20, 2013 by sreemathi.v

1 answer

If $y=\tan^{-1}x$, find $\large {\frac{d^2y}{dx^2}}$ in terms of y alone.

asked Jan 2, 2013 by sreemathi.v

1 answer

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