What is the derivative of y=ln(ln(-5x^5))?

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What is the derivative of y=ln(ln(-5x^5))?

2007-11-01 13:31:43 · 4 answers · asked by Troopa06 1 in Science & Mathematics ➔ Mathematics

4 answers

y=ln(ln(-5x^5))
Let u = ln(-5x^5)
du/dx = (-25x^4)/(-5x^5)

y = ln(u)
dy/du = 1/u

Now, dy/dx = dy/du * du/dx
dy/dx = 1/u * (-25x^4)/(-5x^5)
= 1/(-5x^5) * (-25x^4)/(-5x^5)
= (-25x^4)/(-5x^5)^2

2007-11-01 13:37:04 · answer #1 · answered by -eR!c- 2 · 0⤊ 0⤋

5/(x*ln(-5x^5)) just use the chain rule three times.

2007-11-01 20:38:04 · answer #2 · answered by chad c 2 · 0⤊ 0⤋

yÂ´= 1/ln(-5x^5) * 1/(-5x^5) *(-25 x^4)

2007-11-01 20:40:44 · answer #3 · answered by santmann2002 7 · 0⤊ 0⤋

dy/dx=(1/ln(-5x^5)) (1/(-5x^5)) (-25x^4)
=-25x^4 / [(-5x^5)(ln(-5x^5)]

2007-11-01 20:39:32 · answer #4 · answered by cidyah 7 · 0⤊ 0⤋