How do you differentiate #f(x)=(lnx+3x)(cotx-e^x)# using the product rule?
1 Answer
Apr 17, 2017
Explanation:
#"Given " f(x)=g(x)h(x)" then"#
#f'(x)=g(x)h'(x)+h(x)g'(x)larr" product rule""#
#"here " g(x)=lnx+3xrArrg'(x)=1/x+3#
#"and " h(x)=cotx-e^xrArrh'(x)=-csc^2x-e^x#
#rArrf'(x)=(ln+3x)(-csc^2x-e^x)#
#color(white)(xxxxxxxx)+(cotx-e^x)(1/x+3)#
#color(white)(rArrf'(x))=(cotx-e^x)(1/x+3)#
#color(white)(xxxxxxxx)-(lnx+3x)(csc^2x+e^x)#
