What is the derivative of this function #y=sin^-1(x/3)#?
1 Answer
Apr 6, 2017
Explanation:
I am going to assume that the
Looking at the differentiation of trigonometric functions, the derivative of
Proof:
If#y=arcsin(x)# , then#x=sin(y)# . Differentiating both sides with respect to#x# , we get#1=cos(y)dy/dx# . Then,#dy/dx=1/cos(y)# , which is equal to#1/sqrt(1-sin^2(y))# . But we said that#y=arcsin(x)# , so#dy/dx=1/sqrt(1-x^2)# .
In order to differentiate
Then,