Question

derivatieve of x^2 secy assuming that the equation determines a differentiable function f suht that y= f(x)

Answer 1

technically cant be done

Answer 2

it has to equal something

Answer 3

x^2 secy must equal something

Answer 4

= y^2 +1

Answer 5

x^2 (cosy)^-1 = y^2 +1

Answer 6

rewritting sec as cos^-1

Answer 7

oh i used the product rule

Answer 8

yeh, it is correct

Answer 9

(2x)(secy) but i dont know whts goes in the next bracket

Answer 10

because y depends on x , x^2 (cosy)^-1 needs to be differenitated as product

Answer 11

secytany(x^2)y'

Answer 12

so then it'll be 2yy' = 2xsecy+x^2secytany*y'

Answer 13

so LHS:

let u= x^2
du/dx = 2x
v= (cos(y))^-1
dv/dx = -1 ( cos(y) )^-2 * -sin(y) (dy/dx)

Answer 14

so the LHS = 2x (cosy)^-1 +(x^2sin(y) (sec(y))^2 ) dy/dx

Answer 15

and the RHS will equal 2y dy/dx

Answer 16

\[2xsec(y) +x^2\sin(y)\sec^2(y)\frac{dy}{dx} = 2y \frac{dy}{dx}\]

Answer 17

solve for the dy/dx

Answer 18

ok i understand thank you so much