Question #bbdc7
3 Answers
Explanation:
We will require the use of the chain rule: If
If we let
Note:
If
Explanation:
the standard derivative of
e^x" is " e^x To differentiate
e^(2x)" use the" color(blue)" chain rule"
color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(e^(f(x)))=e^(f(x)) .f'(x))color(white)(2/2)|)))
rArrd/dx(3e^(2x))=3e^(2x).d/dx(2x)=6e^(2x)
see explanation.
Explanation:
color(orange)"Reminder"
ln(xy)=lnx+lny
rArrln(3e^(2x))≠2xln(3e)
"but "ln(3e^(2x))=ln3+lne^(2x)=ln3+2xcancel(lne)
"and "d/dx(ln3+2x)=2
rArrm'(x)=2m(x)=2.3e^(2x)=6e^(2x)