Question

If f(x)=(e^(2x)+1)^1/2 then f'(0)=

Answer 1

We will first find f ` ( x ) using the chain rule:
f ` ( x ) =
`\frac{1}{2 \sqrt{e ^(2x)+1 } } * 2e^(2x) = \frac{e^(2x) }{ \sqrt{e ^(2x) +1} }`
f ` ( 0 ) =
`\frac{e ^(0) }{ \sqrt{e^(0)+1 } } = (1)/( √(2) )`
Answer: f ` ( 0 ) = 1/√2 ( or: √2/2 )