Question

一道求导题y=√(x)/x+100的导数.没个对的

Answer 1

如果是(根号x)/(x+100)呢

利用商法则

(f/g)'=(f'g-g'f)/g^2

=[(x^(1/2))'*(x+100)-(x^(1/2))*(x+100)']/(x+100)^2

=[1/2x^(-1/2)(x+100)-x^(1/2)*1]/(x+100)^2

=x^(-1/2)(50-1/2*x)/(x+100)^2

如果是根号[x/(x+100)]呢

利用链式加商法则

=1/2*[x/(x+100)]^(-1/2) * [x/(x+100)]'

=1/2*[x/(x+100)]^(-1/2) * [1-100/(x+100)]'

=1/2*[x/(x+100)]^(-1/2) *[100/(x+100)^2]