- #1

clm222

my first few questions are for the integral.

first: doesnt the "dx" at the end of an integral mean "in respect to x"? or any toher variable like "dl", in respect to l?

ie: [itex]\int 4x-xj dx=2{x^2}-\frac{j{x^2}}{2}[/itex]?

[itex]\int 4x-xjdj=-x[/itex]

second: if i want to do definite integration from a to b, and i have the second derivative, how to i diplay the lintegrand?

[itex]\int_a^b \int f''(x)dx[/itex]?

or maybe [itex]\int \int_a^b f''(x)[/itex]? i'm not sure

i also have some questions about derivatives, and their notaion.

first: is it bad to have a function 'd', since you will likely counter stuff like [itex]\frac{dd}{dx}[/itex]?

second: for partial derivatives, is it still bad to use 'd', like in my last question?

third: what are the details of using Leibnez's notation for higher order derivatives. can I write (given f(x,y)=z) "[itex]f_{xx}[/itex]" as "[itex]\frac{∂f}{∂x∂x}[/itex]"? or as"[itex]\frac{∂f}{∂{x^2}}[/itex]". same with, say: [itex]f_{xyy}=\frac{∂f}{∂x∂{y^2}}[/itex] or [itex]f_{xxyxx}=\frac{∂f}{∂{x^2}∂y∂{x^2}}[/itex]

same with the "[itex]f_x[/itex]" notation. does [itex]f_{xx}=f_{x^2}[/itex]? [itex]f_{yxx}=f_{y{x^2}}[/itex] or [itex]f_{xxyxx}=f_{{x^2}y{x^2}}[/itex]?

please correct me any of my mistakes, i am not fully familiar with these notations. thank you.