Question

find dy/dx by implicit differentiation

sqrt (x+y) = (5+x^2y^2)

Answer 1

will give medal & fan ... but i want to understand the steps too...

Answer 2

@iambatman @phi @PaxPolaris @mathsails

Answer 3

@Yttrium

Answer 4

someone help me :'(

Answer 5

\[\LARGE \sqrt {x+y} = (5+x^2y^2)\] Ok try your best to take the derivative and I'll help you.

Answer 6

Well I'm not going to wait around all day, I can help you out and I know the answer but I won't help someone who won't help themselves first.

Answer 7

i have something.... \[\frac{ 1 }{ 2\sqrt{x+y} }*(1+\frac{ dy }{ dx })=2x*2y*\frac{ dy }{ dx }\]

Answer 8

except that was wrong

Answer 9

there is a bit of algebra for this one.
How far did you get?
did you find the derivative of the left side? what did you get ?

Answer 10

1/2 (x+y)^-1/2

Answer 11

and at the end of that I would add d/dx

Answer 12

that's what i'm trying to get to one side to solve for

Answer 13

I have to go on the skytrain now

Answer 14

:'(

Answer 15

\[ \frac{d}{dx} u^\frac{1}{2} = \frac{1}{2}u^{-\frac{1}{2}} \frac{d}{dx} u \]

you have the first part, but you need the second part
\[ \frac{d}{dx} u = \frac{d}{dx} (x+y) \]

Answer 16

this is due in 40 mins oh dear lord

Answer 17

the left side is
\[ \frac{1}{2 \sqrt{x+y}} \cdot (1 + \dot{y} )\]

Answer 18

the right side is x^2 d/dx (y^2) + y^2 d/dx(x^2)

Answer 19

solve for \( \dot{y} \)

Answer 20

for the right side you should get
\[ 2 x^2 y \ \dot{y} + 2 x y^2 \]

Answer 21

now it's algebra, solve for \( \dot{y} \)
\[ \frac{1}{2 \sqrt{x+y}} \cdot (1 + \dot{y} ) = 2 x^2 y \ \dot{y} + 2 x y^2 \]