Question #bbdc7

3 Answers
Feb 1, 2017

= 6e^(2x)

Explanation:

We will require the use of the chain rule: If u is a function of x and y is a function of u, then:

(dy)/(dx) = (dy)/(du) (du)/(dx)

If we let u = 2x, then:

d/dx(3e^(2x)) = d/(du)(3e^u) * d/dx(u)

=3e^u * 2 = 6e^u = 6e^(2x). (since d/dx(2x) = 2)

Note:
If y is a function of x, then d/dx(cy) = c(dy)/(dx), where c is a real, nonzero constant.

Feb 1, 2017

6e^(2x)

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)

Feb 1, 2017

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)