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,