Differentiation · Mathematics · WB JEE

If $$x = {e^t}\sin t$$, $$y = {e^t}\cos t$$ then $${{{d^2}y} \over {d{x^2}}}$$ at x = $$\pi$$ is

The value of $${{dy} \over {dx}}$$ at $$x = {\pi \over 2}$$, where y is given by $$y = {x^{\sin x}} + \sqrt x $$ is

Select the correct statement from (a), (b), (c), (d). The function $$f(x) = x{e^{1 - x}}$$

The function $$f(x) = {e^{ax}} + {e^{ - ax}},a > 0$$ is monotonically increasing for

The second order derivative of a sin3t with respect to a cos3t at $$t = {\pi \over 4}$$ is

If $$y = {\tan ^{ - 1}}\sqrt {{{1 - \sin x} \over {1 + \sin x}}} $$, then the value of $${{dy} \over {dx}}$$ at $$x = {\pi \over 6}$$ is

If x2 + y2 = 4, then $$y{{dy} \over {dx}} + x = $$

If $$y = {A \over x} + B{x^2}$$, then $${x^2}{{{d^2}y} \over {d{x^2}}}$$ =

Let $$f(x) = ta{n^{ - 1}}x$$. Then $$f'(x) + f''(x)=0$$, when x is equal to

If $$y = {\tan ^{ - 1}}{{\sqrt {1 + {x^2}} - 1} \over x}$$, then y'(1) =

If $$y = 2{x^3} - 2{x^2} + 3x - 5$$, then for x = 2 and $$\Delta$$x = 0.1 the value of $$\Delta$$y is

The approximate value of $$\root 5 \of {33} $$ correct to 4 decimal places is

Let $$f(x) = {x^3}{e^{ - 3x}},\,x > 0$$. Then the maximum value of f(x) is

If $$\mathrm{U}_{\mathrm{n}}(\mathrm{n}=1,2)$$ denotes the $$\mathrm{n}^{\text {th }}$$ derivative $$(\mathrm{n}=1,2)$$ of $$\mathrm{U}(x)=\frac{\math...

$$ \text { If } y=\tan ^{-1}\left[\frac{\log _e\left(\frac{e}{x^2}\right)}{\log _e\left(e x^2\right)}\right]+\tan ^{-1}\left[\frac{3+2 \log _e x}{1-6 ...

Suppose $$f:R \to R$$ be given by $$f(x) = \left\{ \matrix{ 1,\,\,\,\,\,\,\,\,\,\,\mathrm{if}\,x = 1 \hfill \cr {e^{({x^{10}} - 1)}} + {(x - 1)^2...

Let $${\cos ^{ - 1}}\left( {{y \over b}} \right) = {\log _e}{\left( {{x \over n}} \right)^n}$$, then $$A{y_2} + B{y_1} + Cy = 0$$ is possible for, whe...

The function $$y = {e^{kx}}$$ satisfies $$\left( {{{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}}} \right)\left( {{{dy} \over {dx}} - y} \right) = y{{dy...

If $$y = {\log ^n}x$$, where $${\log ^n}$$ means $${\log _e}{\log _e}{\log _e}\,...$$ (repeated n times), then $$x\log x{\log ^2}x{\log ^3}x\,.....\,{...

If $$x = \sin \theta $$ and $$y = \sin k\theta $$, then $$(1 - {x^2}){y_2} - x{y_1} - \alpha y = 0$$, for $$\alpha=$$

If $$y = {e^{{{\tan }^{ - 1}}x}}$$, then

Let $$g(x) = \int\limits_x^{2x} {{{f(t)} \over t}dt} $$ where x > 0 and f be continuous function and f(2x) = f(x), then

A bulb is placed at the centre of a circular track of radius 10 m. A vertical wall is erected touching the track at a point P. A man is running along ...

Let f(x) > 0 for all x and f'(x) exists for all x. If f is the inverse function of h and $${h'(x) = {1 \over {1 + \log x}}}$$. Then, f'(x) will be

Let f(x) be a derivable function, f'(x) > f(x) and f(0) = 0. Then,

Let $$f(x) = {x^4} - 4{x^3} + 4{x^2} + c,\,c \in R$$. Then

Let $${f_1}(x) = {e^x}$$, $${f_2}(x) = {e^{{f_1}(x)}}$$, ......, $${f_{n + 1}}(x) = {e^{{f_n}(x)}}$$ for all n $$ \ge $$ 1. Then for any fixed n, $${d...

The equation x log x = 3 $$-$$ x

If $$f(x) = {\log _5}{\log _3}x$$, then f'(e) is equal to

Let $$f(x) = {x^m}$$, m being a non-negative integer. The value of m so that the equality $$f'(a + b) = f'(a) + f'(b)$$ is valid for all a, b > 0 is...

Let $$y = {{{x^2}} \over {{{(x + 1)}^2}(x + 2)}}$$. Then $${{{d^2}y} \over {d{x^2}}}$$ is

Let f and g be differentiable on the interval I and let a, b $$ \in $$ I, a < b. Then,

If f(x) = xn, being a non-negative integer, then the values of n for which f'($$\alpha$$ + $$\beta$$) = f'($$\alpha$$) + f'($$\beta$$) for all $$\alph...