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## Differentiation

### Mathematics

#### Previous Years Questions

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If $$y = {e^{{{\tan }^{ - 1}}x}}$$, then
WB JEE 2022
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 po...
WB JEE 2021
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
WB JEE 2021
If the function $$f(x) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1$$ [a &gt; 0] attains its maximum and minimum at p and q respect...
WB JEE 2020
Let $$f(x) = {x^4} - 4{x^3} + 4{x^2} + c,\,c \in R$$. Then
WB JEE 2019
Let f(x) be a derivable function, f'(x) &gt; f(x) and f(0) = 0. Then,
WB JEE 2019
Let f(x) &gt; 0 for all x and f'(x) exists for all x. If f is the inverse function of h and $${h'(x) = {1 \over {1 + \lo... WB JEE 2019 The equation x log x = 3$$-$$x WB JEE 2018 Let$${f_1}(x) = {e^x}$$,$${f_2}(x) = {e^{{f_1}(x)}}$$, ......,$${f_{n + 1}}(x) = {e^{{f_n}(x)}}$$for all n$$ \ge $$... WB JEE 2018 If$$f(x) = {\log _5}{\log _3}x$$, then f'(e) is equal to WB JEE 2017 Let$$f(x) = {x^3}{e^{ - 3x}},\,x > 0$$. Then the maximum value of f(x) is WB JEE 2011 The approximate value of$$\root 5 \of {33} $$correct to 4 decimal places is WB JEE 2011 If$$y = 2{x^3} - 2{x^2} + 3x - 5$$, then for x = 2 and$$\Delta$$x = 0.1 the value of$$\Delta$$y is WB JEE 2011 If$$y = {\tan ^{ - 1}}{{\sqrt {1 + {x^2}} - 1} \over x}$$, then y'(1) = WB JEE 2011 Let$$f(x) = ta{n^{ - 1}}x$$. Then$$f'(x) + f''(x)=0$$, when x is equal to WB JEE 2011 If$$y = {A \over x} + B{x^2}$$, then$${x^2}{{{d^2}y} \over {d{x^2}}}$$= WB JEE 2011 If x2 + y2 = 4, then$$y{{dy} \over {dx}} + x = $$WB JEE 2011 If$$y = {\tan ^{ - 1}}\sqrt {{{1 - \sin x} \over {1 + \sin x}}} $$, then the value of$${{dy} \over {dx}}$$at$$x = {\...
WB JEE 2009
The second order derivative of a sin3t with respect to a cos3t at $$t = {\pi \over 4}$$ is
WB JEE 2009
The value of $${{dy} \over {dx}}$$ at $$x = {\pi \over 2}$$, where y is given by $$y = {x^{\sin x}} + \sqrt x$$ is...
WB JEE 2008
If $$x = {e^t}\sin t$$, $$y = {e^t}\cos t$$ then $${{{d^2}y} \over {d{x^2}}}$$ at x = $$\pi$$ is
WB JEE 2008

## MCQ (More than One Correct Answer)

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Let $$y = {{{x^2}} \over {{{(x + 1)}^2}(x + 2)}}$$. Then $${{{d^2}y} \over {d{x^2}}}$$ is
WB JEE 2020
Let f and g be differentiable on the interval I and let a, b $$\in$$ I, a &lt; b. Then,
WB JEE 2019
If f(x) = xn, being a non-negative integer, then the values of n for which f'($$\alpha$$ + $$\beta$$) = f'($$\alpha$$) +...
WB JEE 2017

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