How do you find the derivative of x/(1+x^2)?
1 Answer
Jan 8, 2016
Explanation:
Use the quotient rule, which states that for a function
f(x)=(g(x))/(h(x))
the derivative of the function is
f'(x)=(g'(x)h(x)-h'(x)g(x))/(h(x))^2
Thus, the derivative of
((1+x^2)d/dx(x)-xd/dx(1+x^2))/(1+x^2)^2
Find each derivative.
d/dx(x)=1
d/dx(1+x^2)=2x
Hence the derivative is equal to
((1+x^2)-x(2x))/(1+x^2)^2
=(1-x^2)/(1+x^2)^2