Question

Find the derivative using the definition of a derivative

Answer 1

Here's my work, i'm stuck on what to do next

Answer 2

@Kainui

Answer 3

should be \[\frac{f(x+h)-f(x)}{h}\]

Answer 4

i your last step too.. you incorporated the \(h\) of the denominator into the square roots.. you can't do that

Answer 5

Oops yes on the (x+h)
and same for the h... faulty distributing haha

Answer 6

You don't have to multiply h into the square roots in the denominator. and when you multiply the top in -2h is supposed to be postive 2h. check you signs?
\[= \frac{ 1+2x + 2h-1-2x }{ h \sqrt{1+2x-2h} + \sqrt{1+ 2x}}\]
Then simplify the top
\[= \frac{ 2h }{ h \sqrt{1+2x-2h} + \sqrt{1+ 2x}}\]
Cancel the h from top and bottom
\[= \frac{ 2 }{ \sqrt{1+2x-2h} + \sqrt{1+ 2x}}\]
Then now you take limit as h approaches 0, so put h=0 into equation

\[= \frac{ 2}{ \sqrt{1+2x-2(0)} + \sqrt{1+ 2x}}\]
\[= \frac{ 2 }{ \sqrt{1+2x} + \sqrt{1+ 2x}}\]

\[= \frac{ 2 }{ 2\sqrt{1+2x} }\]

= \[= \frac{ 1 }{ \sqrt{1+2x}\]

Answer 7

^ yes

Answer 8

Yes got it! Thank you both!

Answer 9

\[= \frac{ 1 }{ \sqrt{1+2x} }\]