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

Question

anonymous · Answer

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

jaweria · Answer

we are looking for derivative of y

jaweria · Answer

can anyone explain this to me step by step please?

jaweria · Answer

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

anonymous · Answer

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)