Question

(2) y=(1-x)(1-2x) (4) y=(2+3x^2)√(1+〖5x〗^2 ) (8) y=log⁡

Answer 1

(2)y'=[(1-x)(1-2x)]'=(1-x)'(1-2x)+(1-x)(1-2x)'=-(1-2x)-2(1-x)=4x-3

(4)y'=6x[1+(5x)^2 ]^0.5 + 0.5[1+(5x)^2]'(2+3x^2)[1+(5x)^2]^(-0.5)

=6x[1+(5x)^2 ]^0.5 + 0.5*2*5x*(5x)'(2+3x^2)[1+(5x)^2]^(-0.5)

=6x[1+(5x)^2 ]^0.5 + 25x(2+3x^2)[1+(5x)^2]^(-0.5)

(8)y'=[ln(1+x^2)/lna]'=(x^2)'/(1+x^2)lna=2x/(1+x^2)lna

开这么多题干嘛.

(2) (ab)'=a'b+ab'

(4) (x^a)'=ax^(a-1) 及 {g[f(x)]}'=g'[f(x)]*f'(x)

(8) (log_a x)'=1/(xlna) 及 {g[f(x)]}'=g'[f(x)]*f'(x)