Exams › JEE Main › Maths

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

1. 1
2. 2
3. 6
4. 0

Correct answer: 0

Solution

The derivative of the function f(x) at x = 0 involves evaluating the contributions of the trigonometric functions, which yield values that result in a zero matrix. Consequently, the derivative f'(0) is zero, making 1/5 f'(0) also equal to zero.

Related JEE Main Maths questions

• If $A$ is a square matrix, then the matrix product $AA^T$ is a
• Let $f(\alpha)=\begin{bmatrix}\cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha\end{bmatrix}$. If $\alpha$, $\beta$, and $\gamma$ are the angles of a triangle, then the product $f(\alpha)f(\beta)f(\gamma)$ is equal to
• Let $A$, $B$, and $C$ be $n\times n$ matrices. Which of the following statements is true?
• Given the matrix $A_\alpha=\begin{bmatrix}\cos\alpha & -\sin\alpha\\ \sin\alpha & \cos\alpha\end{bmatrix}$, which of the following identities is true?
• Let $A$ be a square matrix satisfying $(A-2I)(A+I)=O$. Then $A^{-1}$ equals:
• A square matrix $P$ obeys the relation $P^2=I-P$, where $I$ denotes the identity matrix. If $P^n=5I-8P$, then the value of $n$ is

⚔️ Practice JEE Main Maths free + battle 1v1 →