How do you find the derivative of #y=e^(3x+4)#?

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Answer 1 · 2018-04-09T13:36:33

#3e^(3x+4)#

Given: #y=e^(3x+4)#

Use the chain rule, which states that,

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

Let #u=3x+4,:.du=3 \ dx,(du)/dx=3#.

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

Multiplying those results together, we get,

#dy/dx=e^u*3#

#=3e^u#

Substituting back #u=3x+4#, we get,

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