How do you find the derivative of y=tan(x)y=tan(x) using first principle?

Question

28-08-2014
Mathematics

contestada

How do you find the derivative of y=tan(x)y=tan(x) using first principle?

Respuesta :

Otras preguntas

frosty the snowman was a jolly happy soul / with a corn cob pipe and a button ______ / and two eyes made out of coal

A chef got 30 bags of onions. The red onions came in bags of 4 and the yellow onions came in bags of 6. If the chef got a total of 156 onions, how many bags of

how can scientists determine the 3d structure of a protein? chegg

A universal theme is one that is specific to a given context, writer, culture, or audience. Please select the best answer from the choices provided T F

in a short paragraph, describe what the Harlem Renaissance was and how it changed how African Amer

2. Why were cities like Rome built atop hills? O A. Because there was no other land available OB. For fertile soil O C. To avoid flooding OD D. For defense

Whos your favourite marvel character and why?

Find the 12 th term of an A.P 16, 11, 6, 1,...........

if your engine is flooded with gasoline, you should push the ____ to the floor and hold for _____.

Write an explicit formula for a_na n , the n^{\text{th}}n th term of the sequence 48, 12, 3, ...48,12,3,I need help with this question

Аноним Аноним · Answer 1 · 2014-08-28T13:35:11+02:00

[tex]y=tanx\\\\y'=\lim\limits_{h\to0}\frac{tan(x+h)-tanx}{h}=\lim\limits_{h\to0}\frac{1}{h}\left(\frac{sin(x+h)}{cos(x+h)}-\frac{sinx}{cosx}\right)\\\\=\lim\limits_{h\to0}\frac{1}{h}\left(\frac{sin(x+h)cosx-sinxcos(x+h)}{cosxcos(x+h)}\right)=\lim\limits_{h\to0}\frac{sin(x+h-x)}{hcosxcos(x+h)}\\\\=\lim\limits_{h\to0}\frac{sinh}{hcosxcos(x+h)}=\left[\frac{0}{0}\right]\xrightarrow{l'Hopital's\ rule}\lim\limits_{h\to0}\frac{cosh}{cosxcos(x+h)+hcosx[-sin(x+h)]}\\\\=\frac{cos0}{cosxcos(x+0)}=\frac{1}{cos^2x}[/tex]