Question

find y' assuming that the equation deermines a differentiable function f such that y =f(x) y^2+1=x^2 3y

topic: implicit differentiation

Answer 1

y^2 +1 = x^2 sec y

Answer 2

3y or secy?

Answer 3

take the derivative of both sides wrt x

Answer 4

2yy'=2x sec(y) +x^2 sec(y)tan(y)y'

Answer 5

solve for y' using algebra

Answer 6

amistre hello!

Answer 7

i think it was \[y^2=x^2\sec(y)\] yes?

Answer 8

howdy.... openstudys behaving bad tonight. i go to post and i get screenfreeze

Answer 9

me too!

Answer 10

2y y' = 2x3y + x^2 3 y'
2y y' -x^2 3 y' = 6xy
y'(2y -3x^2) = 6xy

y' = 6xy/(2y-3x^2)

Answer 11

y^2 + 1 = x^2 sec y satellite

Answer 12

so i used the product rule for the x^2 sec y part?

Answer 13

thanks guys

Answer 14

can you guys help me with the question i just posted

Answer 15

yes the product rule. and when you take the derivative of sec(y) make sure to put the y' at the end. i will write it out if you like let me kn ow

Answer 16

i can do it thank you

Answer 17

2yy' = (2x)(secy)+(secy'tany')(x^2)

is it correct?