Partial Differential eqn - method of characteristics
Am going through problems from book and have come across a section of my lecture notes that i don't understand, i'm sure it's something small i'm missing but can't get my head around it.
In lecture notes we solve the wave eqn;
it gets to the General solution which is;
Q(x,t) = F(x-t) +G(x-t)
and then as one of my initial conditions is;
dQ/dx(0,t) = 2 (where this is the partial derivative of Q wrt. x)
i need to find an expression for the dQ/dx, which was written as;
dQ/dx = F'(x+t) + G'(x-t)
i dont understand how this works?
can anyone help?