Question

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

Answer 1

hmm

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

oh okay thank you :)

Answer 8

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

Answer 9

yw