Question

What is the derivative of `5 cos x`?

Answer 1

`-5sinx`

Explanation:

`"using the "color(blue)"standard derivative"`

`•color(white)(x)d/dx(cosx)=-sinx`

`rArrd/dx(5cosx)=-5sinx`

Answer 2

`-5 sin x`

Explanation:

in the function `5 cos x`, one function is being applied to another.

the function `5x` is being applied to the result of the function `cos x`, to give `5 cos x`.

the functions can be separately differentiated:

`(Deltay)/(Deltax) (cos x) = -sin x`

`(Deltay)/(Deltax) (5x) = 5`

then the derivatives can be multiplied together:

`(Deltay)/(Deltax) (cos x) * (Deltay)/(Deltax) (5x) = 5 * -sin x`

`= -5 sin x`