Question

HELP ASAP FIND EACH DERIVATIVE..... 7) 3x^2y^2=4x^2-4xy

8) 5x^3 + xy^2= 5x^3y^3
9)y=(3x^4+5x^3-5)/2x^4-4​

Answer 1

7. (4x - 3xy^2 - 2y) / (3x^2y + 2x).

Explanation:

Implicit differentiation:

7. 3x^2 y^2 = 4x^2 - 4xy

6x * y^2 + 3x^2 * 2y y' = 8x - 4(x y' + y)

6xy^2 + 6x^2y y' = 8x - 4x y' - 4y

6x^2y y' + 4x y' = 8x - 6xy^2 - 4y

y' = (8x - 6xy^2- 4y) / (6x^2y + 4x)

y' = 2(4x - 3xy^2- 2y) / 2(3x^2y + 2x)

= (4x - 3xy^2 - 2y) / (3x^2y + 2x).

Numbers 8 and 9 are done in the same way.

We use the Chain, Product and Quotient rules where applicable.