Consider this way of differentiating...I have never seen it done...but it is an adaptation of logarithimic differentiating so I am sure other people have done it

It goes something like this...say you have ....now say that is difficult to integrate....why not then do this

[math\f^{-1}(y)=u(x)[/tex]

For example this is a way to either be a smart*** on a test if you forget or it is a way I have discovered of proving a trigonometric identity

......say you forget that derivative...well do this

...differentiating we see that

The trig proof comes from the fact taht

Now since

which is a famous identity...this can be done for most things

Another example would be

Forget how to take the derivative of ln(x)? Do this...

Now making the sub we get

which is the derivative of ln((u(x))