7th Grader Learns Calculus: My Story

[[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?

 

[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

 

[HallsofIvy]

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)

sqrt(x)= x^(1/2) not 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?

 

[Redbelly98]

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