# What is the slope of the line normal to the tangent line of #f(x) = x^2e^(x-1)+2x # at # x= 1 #?

##### 1 Answer

#### Explanation:

To find the slope of the normal line, first find the slope of the tangent line at

To find the derivative, you will have to use the product rule.

#f'(x)=e^(x-1)d/dx(2x)+2xd/dx(e^(x-1))+2#

#f'(x)=2e^(x-1)+2xe^(x-1)+2#

Note that

The slope of the tangent line is the value of the derivative at a certain point. In this case it is

#f'(1)=2e^0+2(1)e^0+2=6#

Recall that

Since the slope of the tangent line is