# Multiplication by -1

Remember that putting a negative sign in front of a function means the same thing as multiplying that function by -1.

### Sample Question

Let *g*(*x*) = -*x*^{2}. Then we could think of this function as

*g*(*x*) = (-1)(*x*^{2}),

therefore

*g ' *(*x*) = (-1)(*x*^{2})' = (-1)(2*x*) = -2*x*.

The moral of the story is that the derivative of the negative of *f* is the negative of the derivative of *f*:

(-*f*(*x*))' = -*f ' *(*x*).

### Sample Problem

Let *f*(*x*) = -sin *x*. Then

*f ' *(*x*) = -(sin *x*)' = -cos(*x*).

This is really just a special case of the constant multiple rule, given that -1 is a constant and all.