salut
f(x)= xlnx-1
u= x u'=1
v=lnx v'=1/x formule => u'v+uv'
=> lnx+x*(1/x)
=>lnx+1=f'(x)
f(x)= (x+2)lnx
u= x+2 u'=1
v=lnx v'=1/x formule => u'v+uv'
=> lnx+(x+2)/x
=>lnx+1+2/x= f'(x)
f(x)= x²lnx
u= x² u'=2x
v=lnx v'=1/x formule u'v+uv'
=>2xlnx+x²/x
=> 2xlnx+x= f'(x)
f(x)= (4x²-1)/(2e^x+3)
u= 4x²-1 u'=8x
v=2e^x v'= 2e^x formule => (u'v-uv')/v²
=> (8x(2e^x+3)-[2e^x(4x²-1)])/(2e^x+3)²
=>(16xe^x+24x-[8x²e^x-2e^x]/(2e^x+3)²
=>(16xe^x+24x-8x²e^x-2e^x)/(2e^x+3)²
=>-2[(4x²-8x-1)e^x-12x]/(2e^x+3)²= f'(x)
