Question

If $f\left(x\right)=\sec \left(3x\right)$, then $f^{\prime }\left(\frac{3\pi }{4}\right)=$

• A. $-3\sqrt{2}$
• B. $-\frac{3\sqrt{2}}{2}$
• C. $\frac{3}{2}$
• D. $\frac{3\sqrt{2}}{2}$
• E. $3\sqrt{2}$

Answer 1

The correct option is E $3\sqrt{2}$

Given, $f\left(x\right)=\sec \left(3x\right)$
We get $f^{\prime }\left(x\right)=3\sec \left(3x\right)\tan \left(3x\right)$
Therefore, we get $f^{\prime }\left(\frac{3\pi }{4}\right)=3\sec \left(\frac{9\pi }{4}\right)\tan \left(\frac{9\pi }{4}\right)$

$=3\sec \left(\frac{\pi }{4}\right)\tan \left(\frac{\pi }{4}\right)$

$=3\times \sqrt{2}\times 1$

$=3\sqrt{2}$