Derivative
Tags
Cegep1
Mathematics
Word count
467 words
Reading time
3 minutes
Slope of a tangent line of a function
Also instantaneous rate of change of the function at the tangent point
The derivative of
$\frac{f(x + h) - f(x)}{h}$ is called the **difference quotient**.
$\frac{dy}{dx}$ is called the **differentiation operator**, or formally Leibniz's notation, and means "take the derivative with respect to $x$."
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Under Leibniz's notation we write
Sidedness
Left-side derivative at
Right-side derivative at
$f'(x) = L \iff f'_-(x) = f'_+(x) = L$
Implicit differentiation
Find
- Considering
/ as a function of / - Differentiating as normal using the Chain Rule
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To evaluate
[!example]+ Find
of .
[!example]- Find
of .
Find the slope of the tangent line to the curve
Plug
Properties & theorems
- Product Rule:
- Quotient Rule:
- Power Rule: