Answered

IDNLearn.com: Your reliable source for finding expert answers. Our platform is designed to provide accurate and comprehensive answers to any questions you may have.

Find the derivative of tan(x).

Sagot :

DᴀʀᴋPᴀʀᴀᴅᴏxidn

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Derivative of tan(x) is sec²x

[tex]\qquad \sf  \dashrightarrow \: \therefore \dfrac{d}{dx} ( \tan(x)) = { \sec}^{2} (x)[/tex]

You can check the first principle method of derivation in attachment

View image DᴀʀᴋPᴀʀᴀᴅᴏx
Fieryanswererftidn

[tex]\rightarrow \sf \dfrac{d}{dx} (tan(x))[/tex]

[tex]\rightarrow \sf \dfrac{d}{dx} ( \ \dfrac{sin(x)}{cos(x)} \ )[/tex]

use the quotient rule

[tex]\rightarrow \sf \dfrac{cos(x) * \dfrac{d}{dx} (sin(x)-sin(x)*\dfrac{d}{dx}(cos(x) }{cos(x)^2}[/tex]

[tex]\rightarrow \sf \dfrac{cos(x) * cos(x)-sin(x)*(-sin(x) )}{cos(x)^2}[/tex]

[tex]\rightarrow \sf \dfrac{cos(x)^2+sin(x)^2}{cos(x)^2}[/tex]

[tex]\rightarrow \sf \dfrac{1}{cos(x)^2}[/tex]

[tex]\rightarrow \sf sec(x)^2[/tex]

used formula's :

  • cos²(x) + sin²(x) = 1
  • [tex]\sf \dfrac{1}{cos^2(x) }= sec^2(x)[/tex]
  • [tex]\sf \frac{d}{dx}[/tex] cos(x) = -sin(x)
  • [tex]\sf \frac{d}{dx}[/tex] sin(x)  = cos(x)
  • tan(x) = sin(x)/cos(x)
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.