Differentiation
255 Questions
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1982
Q251
JEE Advanced
Numerical
14 Mar 2026
If $y = f\left( {{{2x - 1} \over {{x^2} + 1}}} \right)$ and $f'\left( x \right) = \sin {x^2}$, then ${{dy} \over {dx}} = ..........$
Correct Answer: $${{2 + 2x - 2{x^2}} \over {{{\left( {{x^2} + 1} \right)}^2}}}\sin {\left( {{{2x - 1} \over {{x^2} + 1}}} \right)^2}$$
1981
Q252
JEE Advanced
Numerical
14 Mar 2026
Let $y = {e^{x\,\sin \,{x^3}}} + {\left( {\tan x} \right)^x}$. Find ${{dy} \over {dx}}$
Correct Answer: $${e^{x\,\sin {x^3}}}\left[ {\sin {x^3} + 3{x^3}\cos {x^3}} \right] + {\left( {\tan x} \right)^x}\left[ {{{2x} \over {\sin x}} + \log \,\tan x} \right]$$
1980
Q253
JEE Advanced
Numerical
14 Mar 2026
Given $y = {{5x} \over {3\sqrt {{{\left( {1 - x} \right)}^2}} }} + {\cos ^2}\left( {2x + 1} \right)$; Find ${{dy} \over {dx}}$.
Correct Answer: $${{dy} \over {dx}} = \left\{ {\matrix{
{{5 \over 3}.{1 \over {{{\left( {1 - x} \right)}^2}}} - 2\,\sin \left( {4x + 2} \right),} & {x < 1} \cr
{ - {5 \over 3}.{1 \over {{{\left( {x - 1} \right)}^2}}} - 2\,\sin \left( {4x + 2} \right),} & {x > 1} \cr
} } \right.$$
1979
Q254
JEE Advanced
Numerical
14 Mar 2026
Find the derivative of
$$f\left( x \right) = \left\{ {\matrix{
{{{x - 1} \over {2{x^2} - 7x + 5}}} & {when\,\,x \ne 1} \cr
{ - {1 \over 3}} & {when\,\,x = 1} \cr
} } \right.$$
at $x=1$
at $x=1$
Correct Answer: $${ - {2 \over 9}}$$
1978
Q255
JEE Advanced
Numerical
14 Mar 2026
Find the derivative of $\sin \left( {{x^2} + 1} \right)$ with respect to $x$ first principle.
Correct Answer: $$2x\,\cos \left( {{x^2} + 1} \right)$$