and
we need to differentiate
with
respect to
University Maths Notes: Calculus – Differentiating Under the Integral Sign
Suppose we have a function of two variablesand
we need to differentiatewith
respect to
This is called differentiating under the integral. Notice the
above formula has the limits as functions ofWe
are integrating with respect to
but
the limits are not values of
They
are functions of
which
imply values ofIf
the limits are pure numbers the first two terms become zero and we
recover the relationship
Example: Differentiate
with
respect to
Example: Differentiate
with
respect to
