Product Rule...5

[nycmathguy]

Calculus
Section 3.2

 

[MathLover1]

f'(x) is correct

f'' (x) should be

 

[nycmathguy]

f'(x) is correct

f'' (x) should be

View attachment 3628

Can you show the math work for f "(x)?

 

[MathLover1]

just take f'(x) and derivate

=(d/dx)(e^x/sqrt(x)+(d/dx)(e^x*sqrt(x))

=e^x/sqrt(x) - e^x/(2x^(3/2))+e^x sqrt(x) + e^x/(2 sqrt(x))

= e^x sqrt(x) + (3 e^x)/(2 sqrt(x))-e^x/(2 x^(3/2)) .....simplify

 

[nycmathguy]

just take f'(x) and derivate

=(d/dx)(e^x/sqrt(x)+(d/dx)(e^x*sqrt(x))

=e^x/sqrt(x) - e^x/(2x^(3/2))+e^x sqrt(x) + e^x/(2 sqrt(x))

I know to find f "(x), I must differentiate f '(x). I got lost in the algebra calculation. Professor Leonard is famous for telling his students: DON'T TAKE CALCULUS TO FAIL ALGEBRA.

= e^x sqrt(x) + (3 e^x)/(2 sqrt(x))-e^x/(2 x^(3/2)) .....simplify

View attachment 3640