Taylor Rodriguez Blog #3

Toward the end of this week we focused in the shortcut to finding a derivative.
There are two rules to follow when using the derivative shortcut
These rules are : * The Constant Rule
• The Power Rule
The constant rule states that the derivative of a constant is 0
Therefore when asked to find a derivative of an equation with a constant the constant will automatically become 0.

The Power rule states that every time you take a derivative you lose a power.
Therefore if you are not taking the derivative of a constant you bring the exponent to the front of the variable and subtract one from the exponent.
The formula that displays this is
d/dx [x^n ] = nx^n-1
Example: d/dx[x^3] = 3x^2

There are many variations of equations that will call for simplification before you can take the derivative

When taking the derivative of a fraction you must simplify the equation by taking the numerator and placing it in front of the x and the exponent behind the denominator will become a negative
Example: d/dx [1/x^2] = x^-2
Then you would proceed to use the shortcut method to find the derivative.

When taking the derivative of a root you will turn the value of the root into a fraction with the exponent of x over the value of the root.
Example: d/dx [cuberoot x] = X^1/3
Then you would proceed to use the shortcut method to find the derivative.
**do not forget that after finding the derivative of a simplified equation you must convert the derivative back to an unsimplified form
Example: d/dx [ x^1/3] = 1/3x^-2/3 = 1/3cuberoot x^2