Differentiate g(t)= (t-sqrt(t))/(t^1/8)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function g(t)= `(t-sqrt(t))/(t^(1/8))` .

g'(t) = `((t-sqrt t)'(t^(1/8)) - (t^(1/8))'*(t - sqrt t))/(t^(1/8))^2)`

=> `((1 - 1/(2*sqrt t))(t^(1/8)) - (1/8)*t^(-7/8)(t - sqrt t))/((t^(1/8))^2)`

=> `(t^(1/8) - 1/(2*t^(3/8)) - (1/8)*t^(1/8) - (1/8)t^(3/8))/(t^(1/4))`

=> `(2*t^(1/8 + 3/8) - (2/8)*t^(1/8 + 3/8) - (1/4)*t^(3/8- 3/8))/(2*t^(1/4 + 3/8))`

=> `((7/4)*sqrt t - (1/4))/(2*t^(5/8))`

=> `(7*sqrt t - 1)/(8*t^(5/8))`

The derivative of `g(t) = (t - sqrt t)/(t^(1/8))` is `g'(t) = (7*sqrt t - 1)/(8*t^(5/8))`

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