How do you differentiate #f(x)= ( x +2sinx )/ ( x - 6)# using the quotient rule?

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Answer 1 · 2018-07-14T04:00:11

#f'(x)=-(10cosx+2sinx+6)/(x-6)^2#

Here ,

#f(x)=(x+2sinx)/(x-6)#

Using Quotient Rule ,we get

#f'(x)=((x-6)d/(dx)(x+2sinx)-(x+2sinx)d/(dx)(x-6))/(x-6)^2#

#=>f'(x)=((x-6)(1+2cosx)-(x+2sinx)(1))/(x-6)^2#

#=>f'(x)=(x+2xcosx-6-12cosx-x-2sinx)/(x-6)^2#

#=>f'(x)=(-10cosx-2sinx-6)/(x-6)^2#

#=>f'(x)=-(10cosx+2sinx+6)/(x-6)^2#