1. ## Differential equations

ok so i've been given the equation
(S=integrate between infinity and 0 and n = pi)

S(sin(ax)/sinh(bx))dx = (n/2b)tanh(na/2b)

and have been told to take a derivative of it in order to evaluate the following

S(xcos(ax)/sinh(bx))dx

am I correct in thinking that i simply need to differentiate the right hand side of the above with respect to a in order to get my answer or should i be differentiating with respect to b as well?

I have been given the result that:

if S (f(t,x)) dt = A(x)

then S {d[f(t,x)]/dx}dt = A'(x)

but wondered if this can be applied to functions with a third variable such that:

if S (F(t,x,y)) dt = A(x,y)

then S {dF/dy +dF/dx}dt = dA/dx + dA/dy

Or am I barking up the wrong tree?

2. Originally Posted by macabre
ok so i've been given the equation
(S=integrate between infinity and 0 and n = pi)
What n? What does that mean here?

3. S(sin(ax)/sinh(bx))dx = (n/2b)tanh(na/2b)

'n' in the above part i have used to represent the value 'pi' as i couldn't find the correct symbol for it

(as in the one thats roughly 22/7, related to circles etc)