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प्रश्न
Differentiate the following w.r.t.x: `(8)/(3root(3)((2x^2 - 7x - 5)^11`
उत्तर
`f(x) = (8)/(3root(3)((2x^2 - 7x - 5)^11`
We rewrite the denominator using exponent notation:
`f(x) = (8)/3(2x^2 - 7x - 5)^(11/3)`
`f(x) = 8/g(x)`
`g(x) = 3(2x^2 - 7x - 5)^(11/3)`
`d/dx(c/g(x)) = -(cxxg' (x))/(g(x))^2`
We use the chain rule to differentiate:
`g(x) = 3(2x^2 - 7x - 5)^(11/3)`
`g'(x) = 3xx11/3(2x^2 - 7x - 5)^(11/3-1)xxd/dx (2x^2-7x - 5)`
`g'(x) = 11(2x^2 - 7x-5)^(8/3)xx(4x-7)`
`f'(x) = - (8xx11(2x^2 - 7x - 5)^(8/3) xx (4x-7))/(3(2x^2 - 7x - 5)^(11/3))^2`
`f'(x) = - (88(4x-7)(2x^2-7x-5)^(8/3))/(9(2x^2 - 7x + 5)^(22/3))`
`f'(x) = -(39.11x - 68.44)/(-2x^2 + 7x + 5)^(11/3)`
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