Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. 3.3 Rules for Differentiation. Colorado National Monument. The derivative of a constant is zero. If the derivative of a function is its slope, then for a constant function, the derivative must be zero.
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Greg Kelly, Hanford High School, Richland, Washington
3.3 Rules for Differentiation
Colorado National Monument
If the derivative of a function is its slope, then for a constant function, the derivative must be zero.
If we find derivatives with the difference quotient:
We observe a pattern:
When we used the difference quotient, we observed that since the limit had no effect on a constant coefficient, that the constant could be factored to the outside.
sum and difference rules:
(Each term is treated separately)
Find the horizontal tangents of:
Plugging the x values into the original equation, we get:
(The function is even, so we only get two horizontal tangents.)
Notice that this is not just the product of two derivatives.
This is sometimes memorized as:
is the second derivative.
is the third derivative.
is the fourth derivative.
Higher Order Derivatives:
(y double prime)
We will learn later what these higher order derivatives are used for.