The Quotient Rule

​
f(x)
x
g(x)
-1
cos
(x)
D
x
​(
f(x)
g(x)
) =
g(x)
′
f
(x) - f(x)
′
g
(x)
2
g(x)
=
1
2
x
-1
cos
(x) -
x
-
1
1-
2
x
2
-1
cos
(x)
=
x
1-
2
x
2
-1
cos
(x)
+
1
2
x
-1
cos
(x)
If
f
and
g
are both differentiable at
x
and
g(x)≠0
, then the derivative of their quotient at
x
is given by the quotient rule shown above. On the graph,
f
is blue,
g
is red,
f(x)/g(x)
is purple, and the derivative of
f(x)/g(x)
is thick purple.

External Links

Quotient Rule (Wolfram MathWorld)

Permanent Citation

Chris Boucher
​
​"The Quotient Rule"​
​http://demonstrations.wolfram.com/TheQuotientRule/​
​Wolfram Demonstrations Project​
​Published: September 28, 2007