Beevers831idn
Answered

IDNLearn.com connects you with a community of experts ready to answer your questions. Get the information you need from our experts, who provide reliable and detailed answers to all your questions.

What is the Derivative of y=sec(x2)y=sec(x^2)?

Sagot :

Konrad509idn
[tex]y=\sec x^2\\ y'=\tan x^2 \sec x^2 \cdot2x\\ y=2x\tan x^2 \sec x^2 [/tex]
[tex]y=sec(x^2)=\frac{1}{cos(x^2)}=[cos(x^2)]^{-1}\\\\y'=-cos(x^2)^{-2}\cdot[-sin(x^2)]\cdot2x\\\\=\frac{1}{cos^2(x^2)}\cdot sin(x^2)\cdot2x=\frac{2xsin(x^2)}{cos(x^2)cos(x^2)}=2x\cdot\frac{sin(x^2)}{cos(x^2)}\cdot\frac{1}{cos(x^2)}\\\\=\boxed{2xtg(x^2)sec(x^2)}[/tex]
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.