OpenStudy (anonymous):

Let sqrt x+sqrt y=11 and y(4)=81. Find y'(4) by implicit differentiation.

OpenStudy (anonymous):

hmm

OpenStudy (anonymous):

\[\sqrt{x}+\sqrt{y}=11\] take the derivative get \[\frac{1}{2\sqrt{x}}+\frac{y'}{2\sqrt{y}}=0\]

OpenStudy (anonymous):

you good from there? you need to find \(x\) , you know \(y=4\)

OpenStudy (anonymous):

can i just asked how you took the derivative i just learn about them so i'm a little new to the subject but yeah i think i can figure it out from there

OpenStudy (anonymous):

i have a few memorized the square root is a very common function, so i know that if \[f(x)=\sqrt{x}\] then \[f'(x)=\frac{1}{2\sqrt{x}}\] i would suggest you memorize it as well

OpenStudy (anonymous):

so that you can get on with your test, quizzes, homework, whatever, quickly while your fellow students are writing \[\sqrt{x}=x^{\frac{1}{2}}\] \[\frac{d}{dx}[x^{\frac{1}{2}}]=\frac{1}{2}x^{-\frac{1}{2}}=\frac{1}{2\sqrt{x}}\]

OpenStudy (anonymous):

oh okay thank you :)

OpenStudy (anonymous):

it never changes, so you might as well just know it, like knowing \(7\times 8=56\)

OpenStudy (anonymous):

yw