# How do you differentiate #f(x)=(x-2)/(x^4+1)#?

##### 2 Answers

#### Explanation:

#"differentiate using the "color(blue)"quotient rule"#

#"given "f(x)=(g(x))/(h(x))" then"#

#f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larr" quotient rule"#

#g(x)=x-2rArrg'(x)=1#

#h(x)=x^4+1rArrh'(x)=4x^3#

#rArrf'(x)=(x^4+1-4x^3(x-2))/(x^4+1)^2#

#color(white)(rArrf'(x))=(8x^3-3x^4+1)/(x^4+1)^2#

#### Explanation:

We could simply use the u/v rule of differentiation, which is

where,

In this question,

On differentiating the function we have,