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

1 Answer
Jim G.
Mar 1, 2017

#f'(x)=-e^xcsc(e^x)cot(e^x)#

Explanation:

#color(red)(bar(ul(|color(white)(2/2)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(2/2)|)))larr" chain rule"#

#"let "u=e^xrArr(du)/(dx)=e^x#

#rArry=cscurArr(dy)/(du)=-cscucotu#

#rArrf'(x)=-cscucotu.e^x#

change u back into terms of x

#rArrf'(x)=e^xcsc(e^x)cot(e^x)#

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