You haven't showed your attempt at a solution, just how you plugged the equation into WolframAlpha.
I would suggest writing out the first several terms of the infinite series for sin(kx) and taking the derivative of those. From there, the connection to k*cos(kx) should be clear.
Homework Statement
Constant area mixing tube with stations (1) and (2) (i.e., (1)-->-->--(2))
At station (1):
- Mixture of two air streams, defined as Primary (p) and Secondary (s)
u_p = 300 m/s
T_p = 900K
u_s = 30 m/s
T_s = 300K
p_1 = 0.1 MPa
(A_p)/(A_s) = 1/3
1-D flow assumed...