How do you differentiate # f(x)=x^7csc(x)# using the product rule?

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Answer 1 · 2015-10-28T07:14:28

#f'(x)= -x^6csc(x)[xcot(x)-7]#

Keep the first factor and find the derivative of the second then add that to the derivative of the first factor and keep the 2nd factor untouched

#f(x)=uv#

#f'(x)=uv'+u'v#

#f(x)= x^7csc(x)#

#f'(x)=x^7(-csc(x) cot(x))+7x^6csc(x)#

Factor out #-x^6csc(x)#

#f'(x)= -x^6csc(x)[xcot(x)-7]#