Derivate this one √(2t+1)

(2t+1)^(1/2) => 1/2(2t+1)^(-1/2) => 1 /(2√(2t+1))

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d/dt [ (2t+1)^(1/2) ]

. . . apply the chain rule

1/2 * d/dt [ 2t + 1 ] * (2t + 1)^(-1/2)

. . . d/dt 2t+1 = 2

1/2 * 2 * (2t + 1)^(-1/2)

(2t + 1)^(-1/2)

1 / (2t + 1)^(1/2)

1 / sqrt(2t + 1)

(√(2t+1))`=½ * 1/√(2t+1) *(2t+1)`=½ * 1/√(2t+1) *2= 1/√(2t+1)