What is the derivative of #e^(2x)#?

2 Answers
Jun 18, 2018

differentiate by parts

Explanation:

Derivative of #e^x=e^x# (always)
then
#dy/dx=e^(2x)#
now multiply the derivative of #2x# with#e^(2x)#
#dy/dx=2x#
=#(n)*x^(n-1)*2#
the final answer
#e^(2x)*2#

Jun 22, 2018

#2e^(2x)#

Explanation:

Given: #d/dx(e^(2x))#.

Let #y=e^(2x)#.

Use the chain rule, which states that,

#dy/dx=dy/(du)*(du)/dx#

Let #u=2x,:.(du)/dx=2#.

Then, #y=e^u,:.dy/(du)=e^u#.

Combining, we get:

#dy/dx=e^u*2#

#=2e^u#

Substituting back #u=2x#, we get the final answer:

#color(blue)(barul(|=2e^(2x)|)#