Question

If `f(x)= cos 4 x` and `g(x) = -3x`, how do you differentiate `f(g(x))` using the chain rule?

Answer 1

`d/dx(f(g(x))=-12sin12x`

Explanation:

As `f(x)=cos4x` and `g(x)=-3x`, `f(g(x))=cos4(-3x)`

According to chain rule

`d/dxf(g(x))=(df)/(dg)xx(dg)/(dx)`

Hence, as `f(g(x))=cos4(-3x)`

`d/dx(f(g(x))=-4sin4(-3x) xx(-3)`

= `12sin(-12x)=-12sin12x`

Answer 2

`-12sin(12x)`

Explanation:

`(df)/(dx)=(df)/(dg)(dg)/(dx)`
`=-4sin(4g(x))xx(-3)`
`=12sin(4(-3x))`
`-12sin(12x)`