A function f(x)f(x)f(x) is defined by f(x)=∫0sin(x)dt1−t2f(x) = \int_{0}^{\sin(x)} \frac{dt}{\sqrt{1-t^2}}f(x)=∫0sin(x)1−t2dt. What is the derivative f′(x)f'(x)f′(x) at x=π/4x = \pi/4x=π/4?
1
1/2
1/\sqrt{2}
\sqrt{2}