Question

Y=36x/(x+3)^2的导数如求，请给出过程，谢谢

Answer 1

商的求导法则： (u/v)'=(u'v-uv')/v² (u=36x, v=(x+3)² )
复合函数求导：y=f(Φ(x))，则y'=f'(t)*t' (t=Φ(x))
y=36x/(x+3)²
y'={ (36x)'(x+3)² -36x*[(x+3)² ]' }/[(x+3)^4] * [(x+3)² ]' 注：[(x+3)² ]'不是在分母上！！
=[36(x+3)² -36x*2(x+3)]/(x+3)^4 * 2(x+3)
={36(x+3)[(x+3) -2x]*2(x+3)}/(x+3)^4 *
=2[(x+3) -2x]/(x+3)²
=2(3-x)/(x+3)²

PS：一楼的，显然是错误答案！！

Answer 2

y=36x/(x+3)^2，
y'=36/(x+3)^2+36x*(-2)/(x+3)^3=[36(x+3)-72x]/(x+3)^3=36(3-x)/(x+3)^3

追问

如何等于这个=36/(x+3)^2+36x*(-2)/(x+3)^3
请给予说明，我有点看不懂啊，谢谢

Answer 3

商的求导法则 (u/v)'=(u'v-uv')/v^2

u=36x v=(x+3)^2

剩下你会了