Question

Turunan dari logaritma alami
d/dx



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Answer 1

ln(x²(3x+2)) = ln(x²) + ln(3x+2)

                   = 2.ln(x) + ln(3x+2)

d( ln(x²(3x+2)) ) = d(2.ln(x) + ln(3x+2))

                          = 2.d(ln(x) + d(ln(3x+2))

turunan dari ln(x) adalah 1/x

lalu kita lakukan subtitusi untuk 3x+2

3x+2 = t ,

= 2/x + d(ln(t))

= 2/x dx + 1/t dt

= 2/x dx + 1/(3x+2) d(3x+2)

= 2/x dx + 1/(3x+2) . 3 . dx

= (2/x + 3/(3x+2))dx

dy/dx = 2/x + 3/(3x+2)

         = (2(3x+2)+3x)/x(3x+2)

         = (6x+4+3x)/x(3x+2)

         = (9x+4)/x(3x+2)

dy/dx = 9/(3x+2) + 4/(x(3x+2))