Question

Find dy/dx of xy=cot^3(y+x)^2

Answer 1

Implicit D!

Answer 2

You need:
what is the derivative of
\[\frac{d}{dx}\cot(x)\]

Answer 3

-csc^2(x)

Answer 4

Ok so what is
\[\frac{d}{dx}xy\] using implicit D? You need the product rule here.

Answer 5

x+y?

Answer 6

well the product rule gives you
(ab)' = ab' + a'b

Answer 7

You can use the chain rule on (x+y)^2 too.

Answer 8

x+y

Answer 9

Oh some angle identity, eh?

Answer 10

ok, so implicit D would have
\[\frac{d}{dx}xy = x\frac{d}{dx}y + y\frac{d}{dx}x\]
which would then be just

\[\frac{d}{dx}xy = x\frac{d}{dx}y + y\]
or in short form
\[\frac{d}{dx}xy = xy^{\prime} + y\]

Answer 11

Implicit D is actually the chain rule but with variables. We don't know what y(x).