then
is
a very familiar result. If however
or
then
differentiating is not so easy. We have to change the base first
to
and
then differentiate. We do this using the relationship
A Level Maths Notes: C4 – Differentiating Exponentials When the Base is Not e
Ifthenis
a very familiar result. If howeverorthen
differentiating is not so easy. We have to change the base first
toand
then differentiate. We do this using the relationship
The last expression is of
the form
which
differentiates to
Applying
this example towe
obtain
Differentiating
only
introduces another factor
to
give
We
can then find tangents and normals in the usual way.
Example: Find the equation
of the tangent and normal to the curve
at
the point with coordinates
For the tangent
so
at the point
For the normal
