Question

d/dx of y^3 = 1 ?

Answer 1

if you take the derivative of y^3 with respect to x, then y^3 will just be a constant

Answer 2

and you know the derivative of a constant right?

Answer 3

right okay yeah 0

Answer 4

right

Answer 5

so d/dx of yx will be x times dy/dx + y dx/dx = y?

Answer 6

wait.... d/dx of yx is not x

Answer 7

There are two ways to think about this.

1) y^3 = 1 = constant --> y = constant (a horizontal line). So, d/dx is the slope, which is 0.
2) y^3 = 1 --> You can do implicit differentiation. You get: \[ 3y^2 \cdot \dfrac {\mathrm{d}y}{\mathrm{d}x} = 0. \]So, ... 0. See how that works?

Answer 8

d/dx of yx <--- treat y as constant

Answer 9

understand the slope argument...

Answer 10

you only use product rule if you're multiplying two functions of x... for example xlnx...x and lnx are both functions of x

Answer 11

but for yx, it's just constant multiple rule

Answer 12

right okay

Answer 13

what about say, d/dx cos (y) times x

Answer 14

cos y is still a constant

Answer 15

like i said before, you just use product rule if you see two or more x

Answer 16

so it would just be cos(y) d/dx x

Answer 17

right

Answer 18

okay thanks

Answer 19

welcome