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Question
Differentiate the following with respect to x.
`5/x^4 - 2/x^3 + 5/x`
Solution
Let y = `5/x^4 - 2/x^3 + 5/x`
`"dy"/"dx" = 5 "d"/"dx" (1/x^4) - 2"d"/"dx"(1/x^3) + 5"d"/"dx" (1/x)`
`= 5"d"/"dx" (x^-4) - 2 "d"/"dx" (x^-3) + 5x^-1`
= 5(-4a-4-1) - 2(- 3x-3-1) + 5(-1)x-1-1
= - 20x-5 + 6x-4 - 5x-2
`= (-20)/x^5 + 6/x^4 - 5/x^2`
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