Question

导数根号X^2-2X+5如何算

Answer 1

y=√(x²-2x+5)

y'=1/[2√(x²-2x+5)]*(2x-2)

=(x-1)/√(x²-2x+5)

这是复合函数,可设u=x²-2x+5,y=√u

u的导数u'=2x-2

y的导数y'=1/(2√u)

根据复合函数链式法则:

y'=1/(2√u)*(2x-2)

=1/(2√u)*2(x-1)

=(x-1)/√u,将x²-2x+5代回u便可

=(x-1)/√(x²-2x+5)