Question

How do I find the derivative of y=√(1+2e^3x)

Answer 1

This is that same thing as \[y=(1+2e ^{3x})^{1/2}\]

Agreed?

Answer 2

ya, I'm just mostly confused as to how to find the derivative of 2e^3x.. is it just 2e^3x? Like would I use the power rule on that term?

Answer 3

So now we use the chain rule, set u= 1+2e^3x

So now we have u^1/2(derivative of u)

The derivative of u^1/2 is 1/2u^-12

So now we have 1/2u^-1/2(derivative of u)

And how we find the derivative of u is chain rule with 2e^3x (1 is irrelevant bc derivative of 1 is 0)