- Topics At a Glance
- Derivatives of Basic Functions
- Constant Functions
- Lines
- Power Functions
- Exponential Functions
- Logarithmic Functions
- Trigonometric Functions
**Derivatives of More Complicated Functions**- Derivative of a Constant Multiple of a Function
**Multiplication by -1**- Fractions With a Constant Denominator
- More Derivatives of Logarithms
- Derivative of a Sum (or Difference) of Functions
- Derivative of a Product of Functions
- Derivative of a Quotient of Functions
- Derivatives of Those Other Trig Functions
- Solving Derivatives
- Using the Correct Rule(s)
- Giving the Correct Answers
- Derivatives of Even More Complicated Functions
- The Chain Rule
- Re-Constructing the Quotient Rule
- Derivative of a
^{x} - Derivative of
*ln*x - Derivatives of Inverse Trigonometric Functions
- The Chain Rule in Leibniz Notation
- Patterns
- Thinking Backwards
- Implicit Differentiation
- Computing Derivatives Using Implicit Differentiation
- Using Leibniz Notation
- Using Lagrange Notation
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

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

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*).

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.