Can you Differentiate tan2 theta !?

Parametric Equation

x= tan theta, y= tan2theta

Find the value if dy/dx when theta= pi/6

I differentiated tan theta got 1/cos theta which is sec? but stuck on the next part

Thx ..

Try the chain rule

Are you asking about or ?

this one

In that case use the chain rule with u = 2theta as suggested. Post your working if you got the wrong answer and we can help you further.

EDIT: Just saw your post above. The argument inside your trig function should still be 2theta. Otherwise you've done it correctly.

Again I got 2/cos2theta

so when (2/cos2theta) / (1/cos theta )

= 2cos theta / cos 2 theta

when i sub pi/6 into the top one i get decimals , but the answer is 6!

Ah, I've seen your problem. Silly me. The derivitive of tan(theta) isn't sec(theta). Try doing that one again.

try differentiating tan with the quotient rule, remembering tanx = (sinx)/(cosx) and see what the standard result for differentiating tan is

checked again same ans whats wrong?

its 2/cos2theta ?

Basically,



which is what you put in the first post. It's what you've calculated for the very first part. I suspect this mistake was carried through into your calculation of which is why you're getting the wrong answer.

its tan 2 theta not just tan theta

yeah, you can use the chain rule afterwards.

answer you want is 2sec²(2x)

I have got this same answer earlier on but it doesn't work for some reason

(1/cosx)/(2sec²(2x) ) = 2cosx/ cos2x so when you sub the pi/6 you dont get 6

I differentiated tan theta got 1/cos theta