Differentiate arcsin(2x) using the fact that 2x=sin(y)
Differentiate implicitly on both sides with respect to x to get: 2=cos(y) • (dy/dx). Divide by cos(y) on both sides to get: dy/dx=2/cos(y). Use the trigonometric identity cos^2(y)+sin^2(y)=1 rearranged to cos(y) = [1-sin^2(y)]^1/2 and substitute this into dy/dx= 2/cos(y) to get dy/dx=2/[1-sin^2(y)]^1/2. Notice that 2x=sin(y) as given initially and substitute to get dy/dx=2/[1-(2x)^2]^1/2. Final answer is d/dx (arcsin(2x)) = 2/(1-4x^2)^1/2
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