# Computing Derivatives

### Topics

## Introduction to Computing Derivatives - At A Glance:

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*).

#### Exercise 1

Find the derivative of the function.

*f*(*x*) = -cos*x*

#### Exercise 2

Find the derivative of the function.

*f*(*x*) = -2*x*^{5}

#### Exercise 3

Find the derivative of the function.

*f*(*x*) = -*e*^{x}

#### Exercise 4

Find the derivative of the function.

*f*(*x*) = -*ln**x*

#### Exercise 5

Find the derivative of the function.

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