Beevers831idn
Answered

From simple questions to complex issues, IDNLearn.com has the answers you need. Get accurate and comprehensive answers from our network of experienced professionals.

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]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.