JEE Main 2022 (Online) 27th June Evening Shift | Differentiation Question 33 | Mathematics

JEE Main 2022 (Online) 27th June Evening Shift

Numerical

-1

If $$y(x) = {\left( {{x^x}} \right)^x},\,x > 0$$, then $${{{d^2}x} \over {d{y^2}}} + 20$$ at x = 1 is equal to ____________.

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JEE Main 2022 (Online) 26th June Evening Shift

Numerical

-1

Let f : R $$\to$$ R satisfy $$f(x + y) = {2^x}f(y) + {4^y}f(x)$$, $$\forall$$x, y $$\in$$ R. If f(2) = 3, then $$14.\,{{f'(4)} \over {f'(2)}}$$ is equal to ____________.

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JEE Main 2021 (Online) 26th August Morning Shift

Numerical

-1

If y = y(x) is an implicit function of x such that log_e(x + y) = 4xy, then $${{{d^2}y} \over {d{x^2}}}$$ at x = 0 is equal to ___________.

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JEE Main 2021 (Online) 17th March Morning Shift

Numerical

-1

If $$f(x) = \sin \left( {{{\cos }^{ - 1}}\left( {{{1 - {2^{2x}}} \over {1 + {2^{2x}}}}} \right)} \right)$$ and its first derivative with respect to x is $$ - {b \over a}{\log _e}2$$ when x = 1, where a and b are integers, then the minimum value of | a² $$-$$ b² | is ____________ .

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