Page 287 - Calculus Workbook For Dummies

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Chapter 15: Ten Things You Better Remember about Differentiation

Note that the numerator of the quotient rule is identical to the product rule except for
the subtraction. For both rules, you begin by taking the derivative of the first thing you
read: the left function in a product and the top function in a quotient.

Linear Approximation

f x 1 +
^ h
Here’s the fancy calculus formula for a linear approximation: l x = _ i
f l _ x 1 _i x - x 1i. If trying to memorize this leaves you feeling frustrated, flabbergasted,
feebleminded, or flummoxed, or fit to be tied, consider this: It’s just an equation of a
line, and its meaning is identical to the point-slope form for the equation of a line you
learned in algebra I (tweaked a bit): y = y 1 + m x - x 1i.
_

“PSST,” Here’s a Good Way to Remember

the Derivatives of Trig Functions

Take the last three letters in PSST and write down the trig functions that begin with
those letters: secant, secant, tangent. Below these write their co-functions, cosecant,
cosecant, cotangent (add a negative sign). Then add arrows. The arrows point to the
$
derivatives, for example, the arrow after secant points to its derivative, sec tan; and
2
the arrow next to tangent points backwards to its derivative, sec . Here you go:
sec → sec ← tan

csc → –csc ← cot