Question

How do you differentiate `cos(pi*x^2)`?

Answer 1

Derivative of `cos(pi*x^2)` is `-2pixsin(pi*x^2)`

Explanation:

We can use Chain rule here. Let `f(x)=cos(pi*x^2)`. Then we can write it as

`f(x)=cosg(x)`, where `g(x)=pi*x^2`.

Then `(df)/(dx)=(df)/(dg)xx(dg)/(dx)`

= `-sin(pi*x^2)xxpixx2x`

= `-2pixsin(pi*x^2)`