Solving f(x) = 5e^(2x+1) with Chain Rule

[char808]

Homework Statement

f(x) = 5e^(2x+1)

Homework Equations

Chain rule, power rule and constant multiplies rule

The Attempt at a Solution

f(x) = 5e^(2x+1) = 5f(x)

e^(2x+1)

f(u) = e^x f'(u) = e^x
g(x)= 2x+1 g'(x) = 2

5f'(x) = 2e^2x+1

=10e^2x+1


Is that the correct way to go about that?

 

[rock.freak667]

Your answer is correct, but you should write it like this

f(x)=e^2x+1

u=2x+1, u'
f(u)=e^u, f'(u)=e^u

f'(x)=f'(u)*u' = 2e^u=2e^2x+1


So that f(x)=5e^2x+1, f'(x) = 5*2e^2x+1=10e^2x+1

You used variables like 'u' and 'g' in a confusing manner.