MR-136 / 136. zadatak

Odrediti prvi izvod sledeće funkcije:

y=e2x-e-3xe5x-e7x

y=e2x-e-3xe5x-e7x

y=e2x-e-3xe5x-e7x=uv

u=e2x-e-3x

v=e5x-e7x

y'=u'·v-u·v'v2

u'=2e2x-e-3x·-3

u'=2e2x+3e-3x

v'=5e5x-7e7x

y'=2e2x+3e-3xe5x-e7x-e2x-e-3x5e5x-7e7xe5x-e7x2

y'=2e7x-2e9x+3e2x-3e4x-5e7x+7e9x+5e2x-7e4xe5x2-2e5xe7x+-e7x2

y'=5e9x-3e7x-10e4x+8e2xe10x-2e12x+e14x

y'=e2x5e7x-3e5x-10e2x+8e10x1-2e2x+e4x

y'=5e7x-3e5x-10e2x+8e8x1-2e2x+e4x

y'=5e7x-3e5x-10e2x+8e8x1-e2x2