Two small topics in higher mathematics

1. Eight-character principle of derivative of composite function: derivative from outside to inside, derivative layer by layer.

Be careful not to leak the layer.

y'=[tan(e^x)]'

=sec^2(e^x)(e^x)'

=sec^2(e^x)*e^x

2. y' = 2 * x/(1+x 2), and the second wizard should be:

y''=(2-2*x^2)/( 1+x^2)^2，

Let y''=0, x 1= 1, x2=- 1.

Points x= 1 and x=- 1 divide the domain of the function into three intervals:

(-infinity,-1), (-1, 1), (1,+infinity),

When x

When-1

When x> is in 1, y''

So x= 1 and x=- 1 are inflection points.