JEE MAIN Differentiation Previous Year Questions (PYQs) – Page 1 of 6
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Let $f(x)=2x+\tan^{-1}x$ and $g(x)=\log_{e}\!\big(\sqrt{1+x^{2}}+x\big),\ x\in[0,3]$. Then
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Solution
The derivative of ${\tan ^{ - 1}}\left( {{{\sin x - \cos x} \over {\sin x + \cos x}}} \right)$, with respect to ${x \over 2}$
, where $\left( {x \in \left( {0,{\pi \over 2}} \right)} \right)$ is :
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If $y=\sec(\tan^{-1}x)$, then $\dfrac{dy}{dx}$ at $x=1$ is equal to :
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Let $f(x)=x^{5}+2x^{3}+3x+1,; x\in\mathbb{R}$, and let $g(x)$ be a function such that $g(f(x))=x$ for all $x\in\mathbb{R}$. Then $\dfrac{g'(7)}{g'(7)}$ is equal to:
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Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f'(x) $ \ne $ 0 for all x $ \in $ R. If $\left| {\matrix{ {f(x)} & {f'(x)} \cr {f'(x)} & {f''(x)} \cr } } \right|$ = 0, for all x$ \in $R, then the value of f(1) lies in the interval :
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If $2x^{y}+3y^{x}=20$, then $\dfrac{dy}{dx}$ at $(2,2)$ is equal to:
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Let y = y(x) be the solution of the differential equation ${{dy} \over {dx}} = 1 + x{e^{y - x}}, - \sqrt 2 < x < \sqrt 2 ,y(0) = 0$ then, the minimum value of $y(x),x \in \left( { - \sqrt 2 ,\sqrt 2 } \right)$ is equal to :
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The local maximum value of the function $f(x) = {\left( {{2 \over x}} \right)^{{x^2}}}$, x > 0, is
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Let $f(x)=\frac{\sin x+\cos x-\sqrt{2}}{\sin x-\cos x}, x \in[0, \pi]-\left\{\frac{\pi}{4}\right\}$. Then $f\left(\frac{7 \pi}{12}\right) f^{\prime \prime}\left(\frac{7 \pi}{12}\right)$ is equal to
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Solution
JEE MAIN
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