# Question #c66f7

##### 1 Answer

Decreasing on

#### Explanation:

The derivative of a function tells us about whether that function is increasing or decreasing.

- If
#dy/dx>0# , then#y# is increasing. - If
#dy/dx<0# , then#y# is decreasing.

So, we need to take the derivative of the function and find when it is positive and when it is negative.

To find the derivative of the given function, we will need the chain rule. In the case of a natural logarithm function, as we have here, we see that:

#d/dxln(x)=1/x" "=>" "d/dxln(u)=1/u*(du)/dx#

So, we have:

#y=ln(1+x^2)" "=>" "dy/dx=1/(1+x^2)*d/dx(1+x^2)=(2x)/(1+x^2)#

So, we need to find when

#(2x)/(1+x^2)=0" "=>" "2x=0" "=>" "x=0#

This,

So, all we have to do is examine

When

#dy/dx|_(x=-1)# #=(2(-1))/(1+(-1)^2)=(-2)/(2)=-1#

Since this is negative, we know that

Similarly, checking