Find the derivative of the function `y = (e^(5u) - e^(-5u))/(e^(5u)+e^(-5u))`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The derivative of y = `(e^(5u) - e^(-5u))/(e^(5u) + e^(-5u))` has to be determined.

`dy/(du)` = `((5*e^(5u) + 5*e^(-5u))*(e^(5u) + e^(-5u)) - (e^(5u) - e^(-5u))*(5e^(5u) - 5e^(-5u)))/(e^(5u) + e^(-5u))^2`

=> `dy/(du)` = `(5*(e^(10u) + e^(-10u) + 2) - 5*(e^(10u) + e^(-10u) - 2))/(e^(5u) + e^(-5u))^2`

=> `dy/(du) ` = `(5*4)/(e^(5u) + e^(-5u))^2`

=> `dy/(du) ` = `20/(e^(5u) + e^(-5u))^2`

The derivative of y = `(e^(5u) - e^(-5u))/(e^(5u) + e^(-5u))` is `dy/(du)` = `20/(e^(5u) + e^(-5u))^2`

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