Question

Find dy/dx implicitly.. ew ;p

Answer 1

\[6e^{xy}-2x=y^2+13x^2\]

Answer 2

Ok this one is long

Answer 3

I'm not good at implicit differentiation... at all! ;/

Answer 4

but try it and see if you can get to this:
\[6e^{xy}\frac{ dy }{ dx }-2y \frac{ dy }{ dx } = 26x-2e^{xy}y\]

Answer 5

^ 2y? it's 2x?

Answer 6

the first term should be
\[6xe^{xy}\frac{ dy }{ dx }\]
I missed the x.

Answer 7

wait can we go step by step.. because I don't even know how to solve implicitly?

Answer 8

I don't want to just give you the answer, but I will start you off, sound good?

Answer 9

I don't wait the answer lol? I want to know the steps of how to solve it?

Answer 10

if you know product rule and chain rule, you are good to start...

Answer 11

I am not sure about the answer but can I join in the topic? I think I first step is to take the derivative on every term on both sides of the equation...

Answer 12

\[6e^{xy} \]

6 is a constant, factor it out.
\[\frac{ dy }{ dx } e^{xy} = e^{xy}\]
this requires chain rule + product rule next.
if you look @ the chain rule, you take the derivative of the function and then whatever is inside the function. or raised function.
\[\frac{ dy }{ dx }(xy) = x (\frac{ dy }{ dx } )y+ y(\frac{ dy }{ dx })x\]

since you are differentiating with respect to x, you just leave y' there
\[ans: x \frac{ dy }{ dx }+ y\]

Answer 13

put it all together, you get:
\[6e^{xy}(x \frac{ dy }{ dx }+y) - .....\]

Answer 14

You do the same for the other functions, use algebra then to solve for dy/dx.
You're answer should look something like:
\[\frac{ dy }{ dx }= \frac{ xy }{ xyz }\]
or some form like that. where you only have x and y on one side and dy/dx on the other.