How do you use the chain rule to differentiate y=cos(6x^2)?

1 Answer
Feb 26, 2017

(dy)/(dx)=-12xcos6x^2

Explanation:

Chain Rule - In order to differentiate a function of a function, say y, =f(g(x)), where we have to find (dy)/(dx), we need to do (a) substitute u=g(x), which gives us y=f(u). Then we need to use a formula called Chain Rule, which states that (dy)/(dx)=(dy)/(du)xx(du)/(dx). In fact if we have something like y=f(g(h(x))), we can have (dy)/(dx)=(dy)/(df)xx(df)/(dg)xx(dg)/(dh)

Here we have y=cos(6x^2) i.e. y=cos(g(x)), where g(x)=6x^2

Hence (dy)/(dx)=d/(dg(x))cos(g(x))xxd/(dx)6x^2

= -sin(6x^2)xx12x

= -12xcos6x^2