Question

Question #6927d

Answer 1

`frac(d)(dx)(cos(4 x)) = - 4 sin(4 x)`

Explanation:

We have: `cos(4 x)`

This expression can be differentiated using the "chain rule".

Let `u = 4 x Rightarrow u' = 4` and `v = cos(u) Rightarrow v' = - sin(u)`:

`Rightarrow frac(d)(dx)(cos(4 x)) = u' cdot v'`

`Rightarrow frac(d)(dx)(cos(4 x)) = 4 cdot (- sin(u))`

`Rightarrow frac(d)(dx)(cos(4 x)) = - 4 sin(u)`

Then, let's replace `u` with `4 x`:

`Rightarrow frac(d)(dx)(cos(4 x)) = - 4 sin(4 x)`

Answer 2

`-4sin(4x)`

Explanation:

`"differentiate using the "color(blue)"chain rule"`

`• d/dx(f(g(x)))=f'(g(x))xxg'(x)`

`rArrd/dx(cos(4x))=-sin(4x)xxd/dx(4x)`

`color(white)(xxxxxxxxxxx)=-4sin(4x)`