Question

Find rhe derivetive of log(tanx) by first principle

Answer 1

Answer:

#d/dx tanx = lim_(h->0) (tan(x+h)-tanx)/h# Using the trigonometric formulas for the sum of two angles: #tan(x+h) = sin(x+h)/cos(x+h)# ...

#tan(x+h) = (tanx+tan(h))/(1-tanx tan(h))# So: ...

#d/dx tanx = (1+tan^2x ) lim_(h->0) tan(h)/h1/(1-tanx tan(h))