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Question
Differentiate the following w.r.t.x: `(8)/(3root(3)((2x^2 - 7x - 5)^11`
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Solution
`f(x) = (8)/(3root(3)((2x^2 - 7x - 5)^11`
Let y = `(8)/(3root(3)((2x^2 - 7x - 5)^11`
let y = `8/3 (2x^2-7x-5)^(-11/3)`
Differentiating w.r.t. x, we get
`dy/dx = 8/3 (-11/3) (2x^2 - 7x-5)^(-11/3-1) . d/dx(2x^2-7x-5)`
`= -88/9 (2x^2-7x-5)^(-14/3).(4x-7)`
`= (-88(4x-7))/(9(2x^2-7x-5)^(14/3))`
`= (-88(4x-7))/9 root3((2x^2-7x-5)^14)`
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