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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
Let `y = 8/(3 root3((2x^2-7x-5)^11))`
Simplify the expression using laws of exponents
`y = 8/(3(2x^2 - 7x - 5)^(11/3))`
`y = 8/3 (2x^2 - 7x - 5)^(-11/3)`
Differentiate with respect to x using Chain Rule
`dy/dx = d/dx [8/3 (2x^2 - 7x-5)^(-11/3)]`
`dy/dx = 8/3 xxd/dx [(2x^2-7x-5)^(-11/3)]`
`dy/dx = 8/3 xx (-11/3)(2x^2-7x-5)^(-11/3-1) xx d/dx(2x^2-7x-5)`
`dy/dx= -88/9 (2x^2-7x-5)^(-14/3) xx (4x-7)`
Bring the negative power to the denominator:
`dy/dx = (-88(4x-7))/(9(2x^2-7x-5)^(14/3))`
`dy/dx = (88(7-4x))/(9(2x^2-7x-5)^(14/3))`
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