Jawaban:
1) a)f(x)=2x^3-3x^2+12x-1
f'(x)=6x^2-6x+12
b)g(x)=(2x^2-x+1)^4
g'(x)= n.U^(n-1).U'
= 4.(2x^2-x+1)^3.(4x-1)
=(16x-4).(2x^2-x+1)^3
c)h(x)=2x+5/x-3
u=2x+5 v=x-3
u'=2 v'=1
h'(x)=u'.v-u.v'/v²
=2(x-3)-(2x+5)1/(x-3)²
=(2x-6)-(2x+5)/(x²-6x+9)
=-11/(x²-6x+9) atau -11/(x-3)²
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Jawaban:
1) a)f(x)=2x^3-3x^2+12x-1
f'(x)=6x^2-6x+12
b)g(x)=(2x^2-x+1)^4
g'(x)= n.U^(n-1).U'
= 4.(2x^2-x+1)^3.(4x-1)
=(16x-4).(2x^2-x+1)^3
c)h(x)=2x+5/x-3
u=2x+5 v=x-3
u'=2 v'=1
h'(x)=u'.v-u.v'/v²
=2(x-3)-(2x+5)1/(x-3)²
=(2x-6)-(2x+5)/(x²-6x+9)
=-11/(x²-6x+9) atau -11/(x-3)²