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Question
Find the derivative of x–4 (3 – 4x–5).
Solution
Let f(x) = x–4 (3 – 4x–5)
By Leibnitz product rule,
f'(x) = `x^-4 d/(dx) (3 - 4x^-5) + (3 - 4x^-5) d/dx(x^-4)`
= x-4 {0 - 4 (-5) x-5-1} + (3 - 4x-5) (-4) x-4-1
= x-4 (20x-6) + (3 - 4x-5) (-4x-5)
= 20x-10 + 12x-5 + 16x-10
= 36x-10 - 12x-5
= `-12/x^5 + 36/x^10`
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