How do i Prove this?

[MEaty]

so i was given a assignment that says that let y=cotx+cot(x)ln(sinx) given that y''=d2y/dx2. i did solve for the first and second derivative but no matter how many tries and techniques i do ang rule i implement, i just cannot prove that this equation y''/csc^3x=-3cotx+2y. i desperately need an explanation

 

[Steven G]

You really did not ask any question. I suspect that given y = cot + cot(x)ln(sinx) that you want to find d²y/d²x.

If you post your work then we can find your mistake and then guide you to the correct answer.

No one on this site will show you how to do this problem, rather we prefer to you solve this problem.

Please post back.

 

[Dr.Peterson]

so i was given a assignment that says that let y=cotx+cot(x)ln(sinx) given that y''=d2y/dx2. i did solve for the first and second derivative but no matter how many tries and techniques i do ang rule i implement, i just cannot prove that this equation y''/csc^3x=-3cotx+2y. i desperately need an explanation

Presumably you found y' and y'' and then substituted into each side of y''/csc^3x=-3cotx+2y to see if it is true. I'm wondering if there might be a typo, after similarly failing but finding the results similar. Please show us (a) the exact wording of the problem as given to you (perhaps an image), and (b) your results for the two derivatives.