1.Differentiate the following

y= (r²6r)e^r

y'=

2.Differentiate the following

P=8e^t

3+5t²

dP/dt

=

3.Differentiate the following

y=x² /x4e^x

dy/dx

=

4.Find the slope of the curve at the givenx-value. Give a decimal answer rounded to three decimal places.

y=x/x²1 ,x=9

5.Find equations of the tangent line and normal line to the given curve at the specified point.

y=4xe^x,(0, 0)

tangent liney=

normal liney=

6.Suppose thatf(5) =1,f'(5) =9,g(5) =2, andg'(5) =3.

Find the following values.

(a)(fg)'(5)

(b)(f/g)'(5)

(c)(g/f)'(5)

7.Differentiate the following

g(x) =3x1/2x+ 1

g'(x) =