Question

Consider the curve x^3 + 3 xy + y^3 = 5
The equation of the tangent line to the curve at the point (1,1) has the form y = mx + b where
m = and b =

Answer 1

Well we first need to differentiate both sides of the equation in your first line.

Answer 2

We do that to so we can find m right? Because the slope would be the derivative

Answer 3

Yes.

Answer 4

The 5 goes away obviously then, let me see if I can figure out how to do the other side!

Answer 5

Can you help me differentiate the x^3 + 3 xy + y^3 without giving it away completely to me? :P

Answer 6

Well I think you can differentiate x^3 w.r.t. x pretty easily using power rule

Answer 7

3(xy)
3 is a constant multiple so use constant multiple rule
3(xy)
xy is a product so use product rule

Answer 8

Okay, so just because it's 3 sums added together doesn't effect the sum rule? I've only seen it used with 2 that's why I got confused

Answer 9

\[\frac{d}{dx}(xy)=y \frac{d}{dx}(x)+x \frac{d}{dx}(y) =y \frac{dx}{dx}+x \frac{dy}{dx}=y(1)+x \frac{dy}{dx} \\ \frac{d(xy)}{dx}=y+x \frac{dy}{dx}=y+xy' \]

Answer 10

\[C \cdot \frac{d(xy)}{dx}=C(y+xy')\]
where C is a constant

Answer 11

Let me work on this I think I get it! Thanks for your help!

Answer 12

Is it wrong to use 3x when doing the product rule instead of using the constant rule? Sorry for all the questions I'm just trying to figure out this stuff completely as I have a midterm tomorrow hahaha

Answer 13

But you still need to use product for (3x)*y

Answer 14

Yes I got 3x+3y after doing the product rule

Answer 15

:(

Answer 16

derivative of y is y'

Answer 17

(3x*y)'=(3x)'y+(3x)(y)'
=3y+(3x)y'
=3y+3xy'

Answer 18

Cant use power rule on that y'? :O

Answer 19

chain rule

Answer 20

y is a function of x
so that is why we say derivative of y w.r.t x is y'

Answer 21

Ohhhhh okay!!!!! Yes

Answer 22

Thanks a ton I got it from here!