Complex Conjugates with sin and cos

[Oaxaca]

I am rather new to the whole idea of complex conjugates and especially operators.

I was trying to understand the solution to a problem I was doing, but the math is confusing me rather than the physics. In the last row of calculations, why does the sin change to a cos, and the d/dx change to what it is. I recognize that n(pi)/L is the first derivative of the inside function for the trig functions, but don't understand how it got there.

Thank you for any help and sorry in advance if I posted this in the wrong section, I'm not positive what section this would fall under.

 

[Mark44]

I am rather new to the whole idea of complex conjugates and especially operators.

I was trying to understand the solution to a problem I was doing, but the math is confusing me rather than the physics. In the last row of calculations, why does the sin change to a cos, and the d/dx change to what it is. I recognize that n(pi)/L is the first derivative of the inside function for the trig functions, but don't understand how it got there.

In the next -to-last line, there is a $\frac{\partial}{\partial x}$ operator. They're taking the partial derivative of what's to the right, with respect to x.

Thank you for any help and sorry in advance if I posted this in the wrong section, I'm not positive what section this would fall under.

 

[Oaxaca]

In the next -to-last line, there is a $\frac{\partial}{\partial x}$ operator. They're taking the partial derivative of what's to the right, with respect to x.

That makes a lot more sense, I didn't realize that the partial would act as an operator for the proceeding sin. However, how do you choose what to apply the operator to? Is that always the order of the formula?

 

[Mark44]

That makes a lot more sense, I didn't realize that the partial would act as an operator for the proceeding sin. However, how do you choose what to apply the operator to? Is that always the order of the formula?

The operator should be applied to the following factor, not the preceding one. The way this is written is a bit confusing to me. An improvement, I believe, would be
$$\frac{\partial}{\partial x}(\sqrt{\frac 2 L} \sin(\frac{n\pi x}{L})$$
IOW, without that ) immediately following the partial derivative.

 

[Oaxaca]

The operator should be applied to the following factor, not the preceding one. The way this is written is a bit confusing to me. An improvement, I believe, would be
$$\frac{\partial}{\partial x}(\sqrt{\frac 2 L} \sin(\frac{n\pi x}{L})$$
IOW, without that ) immediately following the partial derivative.

I got that much (I wrote "proceeding"- improper english on my part, but not a typo ), but I was referring to line six as it seems they move the operator in between the two wave functions, when it was originally outside.