Approximating the Derivative by the Symmetric Difference Quotient
Approximating the Derivative by the Symmetric Difference Quotient
The derivative of a differentiable real function at can be approximated by the symmetric difference quotient, , where is small. Reduce the difference to reduce the error. The symmetric difference quotient is generally a more accurate approximation than the "standard" one-sided difference quotient .
f
a
f(a+d)-f(a-d)
2d
d
d
f(a+h)-f(a)
h