Homework Help: Need some help!

1. Jun 18, 2010

[C]alculus

Last week my teacher realized how bright i was in math for doing some basic trigonometry as a 7th grader. Well actually half of my class knows some trigonometry but why pick me? So she picked some private environment for me to learn calculus, she thinks lessons in regular class is too easy. I wanted to say no but i thought it was going to be interesting.

I just wanted to know if these are right.
(y^2-sin(x)-x^2(y))+(ln x)^2=cos(x)
d/dx(y^2-sin(x)-x^2(y))+2(ln x))=d/dx(cos(x))<-- is that right?
2y(dy/dx)-cos(x)-2x(y)+(x^2)dy/dx+2/x=-sin(x) <-- Messy so yah.
(dy/dx)(2y-x^2)-cos(x)-2x(y)+2/x=-sin(x)
dy/dx(2y-x^2)=-sin(x)+cos(x)+2xy-2/x
dy/dx=(-sin(x)+cos(x)+2xy-2/x)/(2y-x^2)
So am i right?

(xy+x^2)=sqrt(x)
d/dx(xy+x^2)=d/dx((x)^-1)
y+x(dy/dx)+2x=-x^-2
x(dy/dx)=-x^2-y-2x
dy/dx=(x^2-2x-y)/x
How bout this?

2. Jun 18, 2010

miglo

im pretty sure the first one is correct
but the second doesn't seem right to me
for the sqrt(x) try changing it to x^1/2 then differentiate from there

3. Jun 19, 2010

HallsofIvy

sqrt(x)= x^(1/2) not x^-1.

4. Jun 19, 2010

Redbelly98

Staff Emeritus
Moderator's note: thread moved from "Calculus & Analysis"

Homework assignments or any textbook style exercises are to be posted in the appropriate forum in our https://www.physicsforums.com/forumdisplay.php?f=152" area. This should be done whether the problem is part of one's assigned coursework or just independent study.

Last edited by a moderator: Apr 25, 2017