Math help!

[Fenny]

Last couple of exams next week and there is a repeating question in the past papers that I cant do. Ive searched extensivly and cant find the answer

Its the derivation of a product rule in vectors.

Where 'f' is a scaler function and 'A' is a vector point function.

As far as I know I keep getting out all three terms to be the same. There has to be some cancellation somewhere but I cant figure out where and the lecture notes dont help.

Thanks for reading

 

[Fyebot]

Call the grad thing Triangle, because I'm lazy and I'm not gonna try to latex it and find all the symbols etc. Also by d/dx I'm refering to the partial derivative

Let A=(a1, a2, a3), Triangle = (d/dx, d/dy, d/dz)

Triangle.(fA)=dfa1/dx+dfa2/dy+dfa3/dz=(df/dx)a1+f(da1/dx)+(df/dy)a2+f(da2/dy)+(df/dz)a3+f(da3/dz)=A.triangle(f)+f(triangle.A)

(Since f(triangle.A)= f(da1/dx+da2/dy+da3/dz) and A.triangle(f)=A.(df/dx, df/dy,df/dz)=a1(df/dx)+a2(df/dy)+a3(df/dz))

Just look at all the component bits and use the product rule for functions, as f and all the a's are functions. Can do it a bit more tidly by only considering the ith component if you want also.

Hope that helped

 

[Dave]

As far as I can see, it's just use the calculus product rule and simplify? Here's my 2 line working (sorry about the handwriting):

(bottom line is delta f on the right, that's a scribbled out dot)

 

[Jonny69]

MATHS

We're not yankee doodle Americans!!!

Unless it was a typo in which case, carry on.

 

[Fenny]

Thanks a lot guys

Its been a while since I used all the chain, product rule stuff. I also hadn't realised that both changed with x,y,z.

And to Jonny69, I humbly apologize for being so inconsiderate.

 

[Ripper]

Looks like useful stuff for later in life

 

[Fyebot]

Looks like useful stuff for later in life

If you're doing anything in science, engineering, finance, computer science and a boat load of others? Yes

 

[davethe11]

I humbly apologize for being so inconsiderate.

very british, good job