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1. x ^y = y +1
introducing ln on both sides

yln(x) = ln(y) + ln(1)

Let u = y v = ln(x)
du/dy= dy/dx dv/dx= 1/x

ln(x) . dy/dx + y/x = 1/y . dy/dx

ln(x) . dy/dx - 1/y . dy/dx = -y/x
dy/dx [ ln(x) - 1/y] = -y/x

Textbook answer is dy/dx [1/(y+1) + ln(x) ] = y/x
ok for the positive RhS, multiply by (-) throughout the equation before factorising dx/dy but the y+1?
2. oh w8 i think i found my mistake
y+1 doesnt equal to lny + ln 1 but to ln(y+1)
3. (Original post by Carlos Nim)
oh w8 i think i found my mistake
y+1 doesnt equal to lny + ln 1 but to ln(y+1)
Precisely.

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Updated: March 11, 2018
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