By primary school algebra (try it!) girlfriend can show that$$fracf(x+h)-f(x)h=-frac1sqrtx+h+2,sqrtx+2,,(sqrtx+h+2+sqrtx+2)$$and the is then simple to find the limit as $h o0$.
You are watching: Derivative of sqrt(1-x^2)
$$fracddx frac1sqrtx+2=lim_h o0fracleft(frac1sqrtx+h+2-frac1sqrtx+2 ight)h$$
$$=lim_h o0fracleft(frac1sqrtx+h+2-frac1sqrtx+2 ight)h imesfracfrac1sqrtx+h+2+frac1sqrtx+2frac1sqrtx+h+2+frac1sqrtx+2$$
$$=lim_h o0fracleft(frac1x+h+2-frac1x+2 ight)hleft(frac1sqrtx+h+2+frac1sqrtx+2 ight)$$
$$=lim_h o0fracleft(frac-h(x+h+2)(x+2) ight)hleft(frac1sqrtx+h+2+frac1sqrtx+2 ight)$$
$$=lim_h o0fracleft(frac-1(x+h+2)(x+2) ight)left(frac1sqrtx+h+2+frac1sqrtx+2 ight)$$
$$=fracfrac-1(x+2)^2frac2sqrtx+2$$
$$=frac-12(x+2)^frac32$$
re-publishing
cite
follow
answer Jun 2 "16 in ~ 4:48
Ian MillerIan müller
11.5k11 yellow badge2222 silver- badges4040 bronze title
$endgroup$
1
add a comment |
your Answer
Thanks for contributing an answer to katifund.orgematics Stack Exchange!
Please be sure to answer the question. Administer details and share your research!But avoid …
Asking because that help, clarification, or responding to other answers.Making statements based on opinion; back them increase with recommendations or personal experience.Use katifund.orgJax to format equations. katifund.orgJax reference.
To learn more, watch our advice on writing great answers.
See more: Five Letter Words That Begin And End With T, Words That Start With T And End In T
Draft saved
Draft discarded
Sign increase or log in
sign up using Google
authorize up making use of Facebook
sign up utilizing Email and Password
submit
Post as a guest
surname
email Required, yet never shown
Post as a guest
surname
Required, but never shown
short article Your answer Discard
By click “Post her Answer”, friend agree come our terms of service, privacy policy and cookie plan
Not the answer you're looking for? Browse various other questions tagged calculus boundaries derivatives radicals or questioning your own question.
Featured ~ above Meta
Linked
4
Find derivative that $f(x)=frac1sqrtx+2+2x$ by definition
1
Find $frackatifund.orgrmd katifund.orgrmd xfrac1sqrt<3>x+2$ using only the definition of the derivative
connected
0
making use of the limit an interpretation to find a derivative because that $2sqrtx-3$
0
Derivative Proof using Basic meaning
1
finding the derivative using the definition?
5
detect the derivative that $f(x) = frac8sqrtx -2$ using very first principles.
2
just how do you uncover the derivative the $sqrtx^2+9$ using the an interpretation of a derivative?
1
recognize derivative of $fracxx^2+1$ using only the meaning of derivative
1
uncover $frackatifund.orgrmd katifund.orgrmd xfrac1sqrt<3>x+2$ using only the meaning of the derivative
1
utilizing the limit meaning to uncover a derivative because that $frac-5x2+sqrtx+3$
10
detect derivative the $sqrt<3>sin(2x)$ using only meaning of derivative
3
just how to calculate using derivative meaning
warm Network questions much more hot concerns
concern feed
i ordered it to RSS
inquiry feed To subscribe to this RSS feed, copy and paste this URL right into your RSS reader.
katifund.org
company
ridge Exchange Network
site design / logo design © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.10.21.40537
katifund.orgematics stack Exchange works best with JavaScript permitted
her privacy
By click “Accept all cookies”, friend agree ridge Exchange have the right to store cookies on your an equipment and disclose details in accordance through our Cookie Policy.