How do we take the derivative here? y = square root(x^2 + 4x) − x?

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y = [ x² + 4x ]^(1/2) - x
dy/dx = (1/2) [ x² + 4x ]^(-1/2) [ x² + 4x ] - 1
dy/dx = [ x² + 4x ] / [ 2 (x² + 4x)^(1/2) ] - 1

y = sqrt(x^2+4x) - x
y = (x^2+4x)^(1/2) - x
y' = (1/2) (x^2+4x)^(-1/2) d/dx (x^2+4x) - 1
y' = (1/2)(x^2+4x)^(-1/2) (2x+4) - 1
y' = (2x+4) / (2(x^2+4x)^(1/2)) - 1
y' = (2x+4) /(2sqrt(x^2+4x)) - 1

y' = (x+2) / sqrt(x^2+4x) - 1