Question

If y = 2√2secx, then dy/dx at x=π/4 is​

Answer 1

If y = 2√2secx, then dy/dx at x=π/4 is​ 4

Step-by-step explanation:

Given:

$y=2\sqrt{2}\sec x$

To find out:

$\frac{dy}{dx}$ at x = π/4

Solution:

$y=2\sqrt{2}\sec x$

$\implies \frac{dy}{dx}=\frac{d}{dx}(2\sqrt{2}\sec x)$

$\implies \frac{dy}{dx}=2\sqrt{2}\frac{d}{dx}(\sec x)$

$\implies \frac{dy}{dx}=2\sqrt{2}\sec x\tan x$

Thus,

$\implies \frac{dy}{dx}\Bigr|_{x=\pi/4}=2\sqrt{2}\sec \frac{\pi}{4}\tan \frac{\pi}{4}$

$\implies \implies \frac{dy}{dx}\Bigr|_{x=\pi/4}=2\sqrt{2}\times \sqrt{2}\times 1$

$\implies \implies \frac{dy}{dx}\Bigr|_{x=\pi/4}=4$

Hope this answer is helpful.

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Answer 2

Given :   y = 2√2secx

To Find : dy/dx at x=π/4

Solution:

y = 2√2secx

=> dy/dx  = 2√2secxtanx

dy/dx at x=π/4

secπ/4 = √2

tanπ/4 = 1

=> dy/dx  = 2√2√2(1)

=>  dy/dx  =  2(2)

=>   dy/dx  =  4

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