Answered

Join the growing community of curious minds on IDNLearn.com. Discover in-depth and trustworthy answers from our extensive network of knowledgeable professionals.

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)
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.