2.3. Techniques of Differentiation http://www.ck12.org
and
d
dx[f(x)−g(x)] =d
dx[f(x)]−d
dx[g(x)].In simpler notation,
(f±g)′=f′±g′.Example 5:
d
dx[^3 x(^2) + 2 x] = d
dx[^3 x
(^2) ]+d
dx[^2 x]
= (^3) dxd[x^2 ]+ (^2) dxd[x]
= 3 [ 2 x]+ 2 [ 1 ]
= 6 x+ 2.
Example 6:
d
dx[x
(^3) − 5 x (^2) ] = d
dx[x
(^3) ]− 5 d
dx[x
(^2) ]
= 3 x^2 − 5 [ 2 x]
= 3 x^2 − 10 x.
The Product Rule
Iffandgare differentiable atx, then
d
dx[f(x)·g(x)] =f(x)
d
dxg(x)+g(x)
d
dxf(x).
In a simpler notation,
(f·g)′=f·g′+g·f′.
The derivative of the product of two functions is equal to the first times the derivative of the second plus the second
times the derivative of the first.
Keep in mind that
(f·g)′ 6 =f′·g′.
Example 7: