- #1

- 36

- 0

## Homework Statement

Implicit Differentiation:

I Was given the equation find dy/dx:

__(3x__

^{3}y^{2}+ 7x)(x

^{2}y

^{3}+ 3xy)-

## The Attempt at a Solution

Ok, i know i have to use the product rule on top, and on bottom and the quotient rule for the fraction so... if i set

s = 3x

^{3}

t = y

^{2}

u = (3x

^{3}y

^{2}+ 7x)

w = x

^{2}

n = y

^{3}

z = 3x

q = y

v = (x

^{2}y

^{3}+ 3xy)

ds = 9x

^{2}

dt = 2y(dy/dx)

du = (s(dt) + t(ds)) + 7)

dw = 2x

dn = 3y

^{2}(dy/dx)

dz = 3

dq = 1(dy/dx)

dv = (w(dn) + n(dw)) + (z(dq) + q(dz))

Quotient rule: v(du) - u(dv)/(v

^{2})

ok, I'm just making sure i didn't make a mistake.

so now i do:

__(x__

^{2}y^{3}+ 3xy)((3x^{3}(2y(dy/dx)) + y^{2}(9x^{2})) + 7)) - (3x^{3}y^{2}+ 7x)((x^{2}(3y^{2}(dy/dx)) + y^{3}(2x)) + ((3x(1(dy/dx)) + 3y)(x

^{2}y

^{3}+ 3xy)

^{2}

I had a tutor help me out in Implicit Diff. but i still don't really remember this stuff unless i look at it, and i almost always get different from the professor, is the above correct ( without factoring?) it looks alot easier on my paper lol. and i'm supposed to be ready for this kind of magnitude questions on my exam :S i also don't know how i am going to be able to get dy/dx out of my equation, any tips there?