How do you find the derivative of y=arcsin(1/x)?
2 Answers
First, recall the identity
If this identity doesn't look familiar then I may recommend viewing a few videos from this page as they present a couple identities like this, and explain why they are true.
Differentiating
The derivative of
Now, all we need to do is simplify a bit:
Explanation:
We may also know from the outset that:
d/dx"arcsec"(x)=1/(absxsqrt(x^2-1)) d/dx"arccsc"(x)=-1/(absxsqrt(x^2-1))
Then:
y=arcsin(1/x)
sin(y)=1/x
1/(sin(y))=x
csc(y)=x
y="arccsc"(x)
Then:
dy/dx=-1/(absxsqrt(x^2-1))