Find the derivative of the function. y = sin^-1(8x + 1)

Question

Please help me

Answer 1

Let u(x) = 8x +1, so we have a composition y = arcsin(u(x)).  Then the derivative will be, by the Chain Rule, du/dx times d(arcsin(u))/du. 

 

Derivative of arcsin(u) is 1/sqrt(1 + u^2).

 

du/dx is 8.

 

Substituting, we get that the derivative of arcsin(8x+1) is 8/sqrt(1 + (8x+1)^2)