Question

derivative of sqrt(2x + 1)

Answer 1

= derivative of (2x+1)^(1/2)

Answer 2

Dan, can you explain why the first line of your answer is such?

Answer 3

Substitute u = 2x+1

Answer 4

\[\frac{ dy }{ dx }=\frac{ dy }{ du }*\frac{ du }{ dx }\]

Answer 5

Substitute u = 2x+1

so you have

derivative of sqrt(u)

Answer 6

then follow the chain rule as i stated above.

find dy/du and multiply it by du/dx

u = 2x+1
du=2 dx

du/dx=2

Answer 7

Derivative of sqrt u = (1/2)u^(-1/2)

Answer 8

so \[\frac{ 1 }{ 2 }\frac{ 1 }{ \sqrt{u} }*\frac{ du }{ dx } = \frac{ 1 }{ 2 }\frac{ 1 }{ \sqrt{u} }*2\]

Answer 9

now resubstitute back in for u=2x+1

Answer 10

1/sqrt u

Answer 11

thanks for the great explaination, watching some videos on Kahn to better-understand the process

Answer 12

just remember for a parenthesis to a power

just take the derivative of the quantity as a whole, then multiply that by the derivative of the inside of the parenthesis

after doing a couple you will get it down pretty easy

you dont have to do the whole substitution thing in your head