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education/math/MATH1210 (calc 1)/Derivatives.md
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@ -19,3 +19,18 @@ The above formula can be used to find the *derivative*. This may also be referre
A **Secant Line** connects two points on a graph. A **Secant Line** connects two points on a graph.
A **Tangent Line** represents the rate of change or slope at a single point on the graph. A **Tangent Line** represents the rate of change or slope at a single point on the graph.
# Notation
Given the equation $y = f(x)$, the following are all notations used to represent the derivative of $f$ at $x$:
- $f'(x)$
- $\dfrac{d}{dx}f(x)$
- $y'$
- $\dfrac{dy}{dx}$
- $\dfrac{df}{dx}$
- "Derivative of $f$ with respect to $x$"
# Functions that are not differentiable at a given point
- Where a function is not defined
- Where a sharp turn takes place
- If the slope of the tangent line is vertical