Question

derviate y=cos-1(x)

Answer 1

Do you mean\[y = \cos^{-1}x\]

Answer 2

\[\frac{ d }{ dx }\left( \cos ^{-1}x \right)=\frac{ -1 }{ \sqrt{1-x ^{2}} }\]

Answer 3

yeah

Answer 4

Do you need help deriving that tito?
It takes a few weird steps, it's not too bad though.
Touches back on triangle trig math. :b

Answer 5

so give me a detialed answer please

Answer 6

\[\Large y=\arccos x \qquad\to\qquad x=\cos y\]From this form, we'll take the derivative with respect to x,\[\Large 1=(-\sin y)y'\]

Confused about either of those steps? :o

Answer 7

yup what is arc ???!!

Answer 8

\[\arccos x = \cos^{-1}x\]
It's just another way of writing it.

Answer 9

ok no problem keep going

Answer 10

Solving for y' gives us,\[\Large y'\quad=\quad \frac{-1}{\sin y}\]

Answer 11

So from this point, in order to write sin y in terms of x, we need to draw out a triangle from our original relationship x=cos y.

Answer 12

ok great

Answer 13

We drew this setup using this relationship:\[\Large \cos y\quad=\quad\frac{x}{1}\]

Answer 14

Recall that cosine is adjacent/hypotenuse, yes?

Answer 15

yeah right

Answer 16

So let's figure out the length of that missing side.
Remember how to find it using Pythagorean Theorem?

Answer 17

yeah

Answer 18

\[\sqrt{1-^{X2}}\]

Answer 19

Ok good.