Question

Find dy/dx by implicit differentiation.

y^5 + x^2y^3 = 1 + x^4y

So, first I find the derivative:

5y^4 + 2x3y^2 = 4x^3(1)

Now I find dy/dx:

But this is where I don't know what to do?

Please Help.

Answer 1

Did I do the derivative part wrong?

Should it be:

5y^4 + (x^2 . 3y^2 + y^3 . 2x) = (x^4 . 1 + y . 4x^3)

Answer 2

you appear to be very very confused.
y^5 + (x^2)(y^3) = 1 + (x^4)(y)

remember you are finding dy/dx, so you are differentiating with respect to x
Which means that when you differentiate a y term you will have dy/dx tagging along

5y^4 dy/dx + (x^2)(3y^2)dy/dx + (y^3)(2x) = 0 + x^4 dy/dx + y(4x^3)

get all dy/dx terms to the left side

5y^4 dy/dx + 3x^2(y^2) dy/dx - x^4 dy/dx = 4y(x^3) - 2x(y^3)

dy/dx = (4y(x^3) - 2x(y^3)) / (5y^4 + 3x^2(y^2) - x^4 )

check my typing, easy to make an error with all those exponents