Question

4y + xy = 2 find the second derivative.

Answer 1

at (-3,2)

Answer 2

Compute the first derivative first, what do you get?

Answer 3

How do you find the derivative of this. It doesn't look like the derivatives I usually do.

Answer 4

Implicit differentiation

Answer 5

differentiate with respect to x, though, do you know how to do implicit differentiation?

Answer 6

No

Answer 7

You can either proceed by using implicit differentiation or notting that
\[\large 4y+xy = 2\implies y(4+x)=2\implies y=\frac{2}{4+x}\]
and then differentiate like you normally would (using chain rule, of course).

Answer 8

I know how to do normal differentiation. Is it different?

Answer 9

\[\huge \frac{ d }{ dx } 4y + \frac{ d }{ dx } xy = \frac{ d }{ dx}2\]
Use the product rule for xy btw.
it's a bit different

Answer 10

\[\huge 4y' + y + xy' = 0\]
Get the y' on one side and the other terms on the other.
\[\huge y'(4+x) = -y\]
divide
\[\huge y' = \frac{ -y }{ 4+x }\]

Answer 11

Okay and then do I use the quotient rule to find the second derivative?

Answer 12

yeah.

Answer 13

okay one minute

Answer 14

the derivative of -y would just be 0 right?