What is the derivative of this function #y = arcsin(x/2)#?
1 Answer
Dec 4, 2017
# d/dx arcsin(x/2) = 1/(2sqrt(1-x^2/4)) #
Explanation:
Using the known result:
# d/dx arcsin(x) = 1/sqrt(1-x^2) #
In conjunction with the chain rule, we have:
# d/dx arcsin(x/2) = 1/sqrt(1-(x/2)^2) * d/dx (x/2) #
# " " = 1/sqrt(1-x^2/4) * 1/2 #
# " " = 1/(2sqrt(1-x^2/4)) #
