Question

Find dy/dx by implicit differentiation.
x^2−2xy+y^3=2
how do you do this? please show step by step.

Answer 1

take the derivative of x^2

Answer 2

that's easy. 2x

Answer 3

then take the derivative of -2xy using the product rule for differentiating

Answer 4

-2(y+(dy/dx)x)

Answer 5

then take the derivative of y^3

Answer 6

3y^2*(dy/dx)

Answer 7

then the derivative of 2 is 0

Answer 8

so \[2x-2(y+\frac{ dy }{ dx} \times x)+3y ^{2} \times \frac{ dy }{ dx }=0\]

Answer 9

I would multiply the -2 through.

Answer 10

\[2x-2y-2\frac{ dy }{ dx } \times x+3y ^{2} \times \frac{ dy }{ dx }=0\]

Answer 11

then just solve for dy/dx

Answer 12

\[\frac{ 2x - 2y }{ 2-3y ^{2} }=\frac{ dy }{ dx }\] I believe

Answer 13

so dy/dx means derivative of y dividhated by the derivative of x correct? i'm just trying to see how you knew to substitute that notation in at that point

Answer 14

no, dy/dx means the derivative of y in respect to x

Answer 15

for example, we say that the derivative of x is 1 but really it's dx/dx

Answer 16

which equals 1