Question

Find dy/dx by implicit differentiation. 7y sin(x^2) = 9x sin(y^2)

Answer 1

take the derivative of every term, from left to right. use the chain rule (including y') and the product rule well...

Answer 2

Left side...

Answer 3

would dy/dx of 7y be 7yprime or yprime

Answer 4

7 y'

Answer 5

okay thanks

Answer 6

ready for left side?

Answer 7

do you mean the right?

Answer 8

No, I meant left, to check in. Did you get:

7 y' sin(x^2) + 7 y cos(x^2) 2x

Answer 9

yes :D

Answer 10

Great, let me know if you have any questions about the right or solving for y'

Answer 11

would it be like (9x)(cos(2y)(yprime)+(9)(sin(y^2)

Answer 12

(9x)(cos(2y)(yprime)+(9)(sin(y^2)

Chain rule error. When you do the f'(g(x)) part of the chain rule, re-write the inner function - the y^2 without taking its derivative yet (next post I'll show you)

Answer 13

9x cos(y^2) 2y y' + 9 sin(y^2)

Answer 14

okay i see where i messed up

Answer 15

then i isolate \[y^l\]

Answer 16

yes

Answer 17

okay im not sure if i did it right

Answer 18

\[-9x[\sin(y^2)]+7y[\cos(x^2)] / 9x[\cos(y^2)\times2y]+7[\sin(x^2)]\]

Answer 19

is that right

Answer 20

wait its wrong

Answer 21

I think I found two errors in the numerator and added parentheses:
(−9 [sin(y2)]+7y 2x [cos(x2)])/(9x[cos(y2)×2y]+7[sin(x2)])

Answer 22

is that right?

Answer 23

what you said