How do you differentiate #f(x)=e^cot(1/x) # using the chain rule?

Question

1862 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-29T22:21:20

#d/dxe^(cot(1/x))=(e^cot(1/x)csc^2(1/x))/x^2#

Chain rule for #e^(f(x))#:

#d/dxe^(f(x))=e^(f(x))xxf'(x)#

Chain rule for #cot(f(x))#:

#d/dxcot(f(x))=-csc^2x xx f'(x)#

#d/dxe^(cot(1/x))=e^cot(1/x)-csc^2(1/x)-x^-2#

#=e^cot(1/x)csc^2(1/x)x^-2#

#(e^cot(1/x)csc^2(1/x))/x^2#