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Derivation Rules
© 2013 / Mario Konrad
Name
Function
Derivative
Power
x
n
x^n
n
*
x
n
−
1
n * x^{n-1}
Product
f
(
x
)
*
g
(
x
)
f(x) * g(x)
f
(
x
)
*
g
′
(
x
)
+
f
′
(
x
)
*
g
(
x
)
f(x) * g'(x) + f'(x) * g(x)
Sum
f
(
x
)
+
g
(
x
)
f(x) + g(x)
f
′
(
x
)
+
g
′
(
x
)
f'(x) + g'(x)
Scale
a
*
f
(
x
)
a * f(x)
a
*
f
′
(
x
)
a * f'(x)
Reciprocal
1
g
(
x
)
\frac{1}{g(x)}
−
g
′
(
x
)
g
2
(
x
)
-\frac{g'(x)}{g^2(x)}
Quotient
f
(
x
)
g
(
x
)
\frac{f(x)}{g(x)}
f
′
(
x
)
*
g
(
x
)
−
f
(
x
)
*
g
′
(
x
)
g
2
(
x
)
\frac{f'(x) * g(x) - f(x) * g'(x)}{g^2(x)}
Chain (outer times inner)
f
(
g
(
x
)
)
f(g(x))
∂
y
∂
g
*
∂
g
∂
x
\frac{\partial y}{\partial g} * \frac{\partial g}{\partial x}