Question

急求这几个函数的导数

f(x)=2000e^(-o.2x)
g(x)=6x^2 In(2x)

Answer 1

f‘(x)=2000×[e^(-o.2x)]‘× (-0.2x)'
=2000e^(-o.2x)× (-0.2)
=-400e^(-o.2x)

g'(x)=(6x² )'× In(2x)-(6x²)× [In(2x)]'(2x)'
=12x In(2x)-6x² * 1/2x * 2
=12x In(2x)-6x

Answer 2

这里用到两个导数公式就好了
（a^x）'=(a^x)X'(x)'=[(a^x)lna]X(x')
(ab)'=a'Xb+b'Xa

f'(x)=2000*[e^(-o.2x)]'* (-0.2x)'
=2000e^(-o.2x) (-0.2)
=-400e^(-o.2x)

g'(x)=(6x² )'In(2x)-(6x²)[In(2x)]'
=12x*ln(2x)-(6x^2) *(1/2x)*2
=12x In(2x)-6x
(“*”)是乘号

Answer 3

f(x)=2000e^(-o.2x) f'(x)=2000×[e^(-o.2x)]'× (-0.2x)=2000e^(-o.2x)× (-0.2)=-400e^(-o.2x)
g(x)=6x^2 In(2x) g'(x)=6x² )'× In(2x)-(6x²)× [In(2x)]'(2x)' =12x In(2x)-6x² * 1/2x * 2=12x In(2x)-6x