Lindsey's Reflection

This week we learned about implicit derivatives.

implicit means that is it not solved for y. while
an explicit function is solved for y.

whe you take a derivative you must put a notation by every variable
except x.

dy/dx means the the derivative of y
with respect to x. it can also
show up as y^1 which is y prime.

here are the steps to finding an implicit derivative:

1. differentiate both sides with
respect to x--d_/dx

2. collect all dy/dx terms on one
side and move the other terms to
the other side.

3. factor out a dy/dx

4. solve for dy/dx

5. simplify and if it is possible
to do so replace with the original
equation that was given.

here is an example


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

3y^2dy/dx+2ydy/dx-5dy/dx-2x=0

3y^2dy/dx+2ydy/dx-5dy/dx=2x

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

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

and that is the final
answer.
it sometimes is a long process
by ultimately it is very
easy to do.