How to properly take the derivative of the arcsin funciton.

Question

I was given the function f(y)=arcsin(y^5)

 

I tried to take the derivative by

1/sqrt(y^2+1) *5y^4

then I put the derivative of the inner function on top since they are multiplying each other but I still got the question wrong. would you please help me figure out where I went wrong please?

Answer 1

Your radicand (what is under the square root symbol) is not correct. It should be 1-(y^5)^2 = 1-y^10

So it would be (1/sqrt(radicand))*5y^4

%MCEPASTEBIN%

Answer 2

f(x) =arcsin(x) then f(x)' = 1/sqrt(1-x²).

f(x)= arcsin(u(x)) then f(x)'=u'/sqrt(1-u²).

 

here, u = y⁵ and u'=5y⁴

f(y)'= 5y⁴/sqrt(1-y¹⁰)