Product Rule...1

[nycmathguy]

Calculus
Section 3.2

 

[MathLover1]

y=(e^x+2)(2e^x-1)

(d/dx)((e^x+2)(2e^x-1))

=(d/dx)((e^x+2)*(2e^x-1)+(d/dx)(2e^x-1)*(e^x+2)

= e^x*(2e^x-1)+ 2e^x*(e^x+2)

= 2e^(2x) - e^x+ 4 e^x + 2e^(2 x)

= 4e^(2x) - e^x+ 4 e^x

=3e^x + 4e^(2 x)

so

 

[nycmathguy]

y=(e^x+2)(2e^x-1)

(d/dx)((e^x+2)(2e^x-1))

=(d/dx)((e^x+2)*(2e^x-1)+(d/dx)(2e^x-1)*(e^x+2)

= e^x*(2e^x-1)+ 2e^x*(e^x+2)

= 2e^(2x) - e^x+ 4 e^x + 2e^(2 x)

= 4e^(2x) - e^x+ 4 e^x

=3e^x + 4e^(2 x)

so
View attachment 3641

Are you serious? I got this one wrong, too?