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### Derivatives Posted: August 24th, 2011, 1:04 pm
The derivative of with respect to x is the function and is defined as, Example First plug the function into the definition of the derivative. Multiply everything out  So the derivative is ### Re: Derivatives Posted: October 18th, 2011, 10:08 pm
this is the alternate definition of the derivative.

### Re: Derivatives Posted: October 23rd, 2011, 9:01 pm

### Re: Derivatives Posted: October 23rd, 2011, 9:02 pm
Rule 1: Derivative of a Constant

If c is a constant, then

Rule 2: Power Rule for a Positive Integer Powers of x

If n is a positive integer, then nxn−1

Rule 3: The Constant Multiple Rule

If u is a differentiable function of x and c is a constant, then

Rule 4: The Sum and Difference Rule

If u and v are differentiable functions of x, then their sum and differences are differentiable at every point where u and v are both differentiable. At such points,

1.

2.

Rule 5: The Product Rule

If the products of two differentiable functions u and v is differentiable and...

 u = first factor v = second factor

(first) · (second)' + (second) · (first)'

Finding Horizontal Tangents:

Horizontal tangents occur when the slope of the derivative equals zero.

Rule 6: The Quotient Rule

At a point where v ≠ 0, the quotient of two differentiable functions is differentiable and...

u = numerator part of quotient
v = denominator part of quotient

### Re: Derivatives Posted: November 12th, 2011, 12:39 pm
Derivatives of the Six Trig Functions

### Re: Derivatives Posted: November 16th, 2011, 12:26 am
Chain Rule

useful when asked to find the derivative of compositions such as

Method 1: "outside-inside" rule

•    ( 2 )
deriv of outside      deriv of inside
leave inside alone

Method 2:

Examples coming soon

### Re: Derivatives Posted: November 19th, 2011, 10:09 pm
Finding parametrically:

### Re: Derivatives Posted: December 5th, 2011, 5:05 pm
Derivatives of Inverse Trig Functions

is exactly the same except it's negative.

is exactly the same except it's negative.

is exactly the same except it's negative. ### Re: Derivatives Posted: December 8th, 2011, 8:42 am  note: each will be multiplied by