IF y = sin-1 (2x+1/1+4x) find dy/dx

y=sin-12x+11 +4x = sin-12x.21+22xLet 2x = tanθθ = tan-1(2x)Now, y = sin-12tanθ1+tan2θ = sin-1(sin2θ) = 2θ=2tan-1(2x)thus,dydx=211+22x×2xlog2 (using dtan-1xdx=11+x2)

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