Differentiating Inverse Trigonometric Functions
If
then we cannot find
directly. Instead we take the sin of both sides to obtain
and differentiate implicitly using the chain rule. We obtain
Since originally
was given as a function of
we would normally findas a function of
We can do this for
using the identity
We rearrange this to make
the subject:
Hence
If
then we cannot finddirectly. Instead we take the cos of both sides to obtain
and differentiate implicitly using the chain rule. We obtain
Since originallywas given as a function ofwe would normally findas a function ofWe can do this forusing the identityWe rearrange this to make
the subject:
Hence
If
then we cannot finddirectly. Instead we take the
of both sides to obtain
and differentiate implicitly using the chain rule. We obtain
Since originallywas given as a function ofwe would normally findas a function ofWe can do this for
using the identity
Hence