Inverse trigonometric function

[noypihenyo]

Find dy
dx


1.) y = In __x2 (x+1)___
(x + 2)3

2.) y = x3 ( 3lnx-1)

3.) y = __cos6 2x__
(1-sin2x)3


4.) y = __tan 2x__
1- cot 2x


5.) y = x e (exponent pa po ng e) sin2x


6.) Arc tan ____x_______
a- √ a2-x2


7.) __x_______ _ Arc sin _x_
a-√ a2-x2 a

_________
8.) Arc tan /__3x - 4_
√ 4
_______
9.) Arc cos ( 1 - _x_+ √ 2ax-x2
a

pls help i need the answer October 8

 

[quasar987]

3) and 4) are not about inverse functions. Show us what you have tried that didn't work.

For the rest, there is a clever trick you can apply for all of them. Say I want to find the derivative of y(x) = ln(x). since ln(x) is the inverse function of $e^x$=exp(x), I begin by "taking both sides into the argument of exp(x)", such that the equation becomes $e^y=e^{ln(x)}=x$. And now I differentiate both side wrt x: $\frac{d}{dx}e^y=\frac{d}{dx}x$. I use the chain rule on the left hand side: $e^y\frac{dy}{dx} = 1$, or, now replacing y by ln(x): $\frac{dy}{dx} = 1/e^{ln(x)}=1/x$. I suggest you study this exemple until you understand each step. Then, try one of your problems. If you get stuck, you can ask us for help by writing exactly what you've done and where you're stuck.