## Jaweria 2 years ago Need help with this Question I worked on it but its giving me a weird answer. Find Y Prime: Y=cos^-1(2x+5).

1. Aani

$-1/\sqrt{(x-2)(3-x)}$

2. Jaweria

we are looking for derivative of y

3. Jaweria

can anyone explain this to me step by step please?

4. Jaweria

$Y=\cos^{-1} (2x+5)$

5. SinginDaCalc2Blues

This one is a little tricky...Remember the derivative of the inverse cos of (x) or cos^-1(x) is equal to -1/(square root of 1-x^2)... to make this problem more visually appealing, you can let 2x-5=u, you don't have to do this but it makes seeing the solution easier... Now remember there is going to be a chain rule involved... so d/dx of cos^-1(u) is equal to -1/(square root of 1-u^2) and multiplied by the derivative of (2x+5) which is equal to simply 2, because of the chain rule... So what you now have is -1/(square root of 1-u^2) times 2... You can now write that as -2/(square root of 1-u^2)... Then you can simply replace "u" for the original (2x+5) which would look like... -2/(square root of 1-(2x+5)^2)... So that is your final answer!... You can of course simplify it further but I think most teachers would accept this as the final answer...Hope this helps! Again, final answer: -2/(square root of 1-(2x+5)^2)