Since $t$ is the variable and $e^{-\alpha^{2} k^{2} t}$ and $\sin kx$ are constants, we apply the chain rule of differentiation. The derivative of $e^{-\alpha^{2} k^{2} t}$ with respect to $t$ is $-\alpha^{2} k^{2} e^{-\alpha^{2} k^{2} t}$ and the derivative of
Show more…