Find the derivative: x((2x+1)^.5)?

Answer 1

Use the multiplication rule. if you have f(x)g(x)
then the answer is f ' (x)g(x) + f(x)g ' (x)

also, don't forget the chain rule

therefore

f ' (x) = ((2x+1)^.5) + x(.5(2x+1)^-.5)2)
f ' (x) =((2x+1)^.5) + x((2x+1)^-.5))

Answer 2

x √(2x + 1)

product rule:

d/dx (uv) = u'v + v'u

d/dx (x) √(2x + 1) + d/dx √(2x + 1) x

d/dx (x) = 1

√(2x + 1) + d/dx √(2x + 1) x

use the chain rule:
let u = 2x + 1
then d/du (u) = 1/(2√u)
d/dx (2x + 1) = 2

√(2x + 1) + 1/(2√(2x + 1)) * 2 * x

√(2x + 1) + x/√(2x + 1) <== answer

Answer 3

x/(2x+1)^.5 + (2x+1)^.5