We often have to
differentiate functions. For functions of the form
it
is as simple as multiplying by the power and subtracting one from the
power.
it
is as simple as multiplying by the power and subtracting one from the
power.
Example:
This extends to multiples
and sums of powers of
If
we remember that
and
that when differentiating for these functions too we multiply by the
power and subtract one from the power then,
If
we remember that
and
that when differentiating for these functions too we multiply by the
power and subtract one from the power then,
The process is the same for
all powers of
fractions
and negative powers included:
fractions
and negative powers included:
Whatever form the question
is given it we must expression the function to be differentiated in
the form
For
example,
For
example,
We write this as
then
then
These are some more
examples,
Differentiation is used to
find rates of change (when we differentiate with respect to time),
gradients, slopes, tangents and normals.
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