If f(x)=| ccc 2 cos ⁴ x 2 sin ⁴ x 3+ sin ² 2 x 3+2 cos ⁴ x 2 sin ⁴ x sin ² 2 x 2 cos ⁴ x 3+2 sin ⁴ x sin ² 2 x |, then 1/5 f^()(0)= is equal to:

Limit, Continuity and Differentiability: JEE Main 2024 Mathematics question

JEE Main 2024 · 30 Jan, Morning shift · Q3712

JEE Main 202430 Jan, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

f(x)=\left|\begin{array}{ccc} 2 \cos ^4 x & 2 \sin ^4 x & 3+\sin ^2 2 x \\ 3+2 \cos ^4 x & 2 \sin ^4 x & \sin ^2 2 x \\ 2 \cos ^4 x & 3+2 \sin ^4 x & \sin ^2 2 x \end{array}\right|,

then

\frac{1}{5} f^{\prime}(0)=

is equal to :

JEE Main 2024 · 30 Jan, Morning shift · Q3712

JEE Main 202430 Jan, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

f(x)=\left|\begin{array}{ccc} 2 \cos ^4 x & 2 \sin ^4 x & 3+\sin ^2 2 x \\ 3+2 \cos ^4 x & 2 \sin ^4 x & \sin ^2 2 x \\ 2 \cos ^4 x & 3+2 \sin ^4 x & \sin ^2 2 x \end{array}\right|,

then

\frac{1}{5} f^{\prime}(0)=

is equal to :