find the derivative of the function y=xsin(2/x)

Question

anonymous · Answer

can you show steps by steps please thanks

anonymous · Answer

dy/dx = sin2/x   - 2* xcos(2/x) *1/x^2

lalaly · Answer

you differentiate x first and leave sin (2/x) the same + yu leave x and differentiate sin(2/x)
and u get what ishaan got

anonymous · Answer

so how do i compute that..is that all i have to do?

lalaly · Answer

yess whenever u hav to differentiate two functions multiplied by each other
yu differentiate the first one  and write down the second one like itis then u differentiate the second and leav thefirstas it is,,
and add them
first u differentiate x which is 1
so u get sin(2/x)
then yu differentiate only sin (2/x) and leave x
u get x cos(2/x) * -2/x^2

and u add both

sin(2/x) + x cos(2/x) * -2/x^2

anonymous · Answer

so thats the answer?

lalaly · Answer

yup

lalaly · Answer

u  can simplify it yu get
 
sin (2/x) - 2/x cos(2/x)

anonymous · Answer

ok..its just hard but ill practice.. thanks

lalaly · Answer

http://www.analyzemath.com/calculus/Differentiation/rules.html this could help, what i did is calld the product rule...