How do you differentiate f(x) =arcsin(2x + 1) ?

1 Answer
Konstantinos Michailidis
Feb 4, 2016

It is f'(x)=2/(sqrt(1-(2x+1)^2))

Explanation:

Let u(x) = 2x + 1, function f may be considered as the composition f(x) = arcsin(u(x)). Hence we use the chain rule,
f '(x) = ((du)/dx) (d(arcsin(u)))/(du),
to differentiate function f as follows

f'(x)=((2x+1)/dx)*(1/(sqrt(1-u^2))) => f'(x)=2/(sqrt(1-(2x+1)^2))

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