posted by Chelsea on .
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?
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)
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