Calculus Derivative Guide

5.0(1)
studied byStudied by 2 people
5.0(1)
full-widthCall with Kai
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
GameKnowt Play
Card Sorting

1/35

encourage image

There's no tags or description

Looks like no tags are added yet.

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced
Call with Kai

No study sessions yet.

36 Terms

1
New cards

Derivative of sin x

cos x

<p><sup>cos x</sup></p>
2
New cards

Derivative of cos x

-sin x

<p>-sin x</p>
3
New cards

Derivative of tan x

sec2 x

<p>sec<sup>2 </sup>x</p>
4
New cards

Derivative of cot x

-csc2 x

<p>-csc<sup>2 </sup>x</p>
5
New cards

Derivative of sec x

sec x tan x

<p>sec x tan x</p>
6
New cards

Derivative of csc x

-cot x csc x

<p>-cot x csc x</p>
7
New cards

Derivative of ex

ex

<p>e<sup>x</sup></p>
8
New cards

Product Rule

f(x)*g’(x) + g(x)*f’(x)

<p><span>f(x)*g’(x) + g(x)*f’(x)</span></p>
9
New cards

Quotient Rule f(x) / g(x)

(g(x)*f’(x) - f(x)*g’(x)) / (g(x))2

<p><span>(g(x)*f’(x) - f(x)*g’(x)) / (g(x))</span><sup>2</sup></p>
10
New cards

Power Rule (derivative of xn)

nxn-1

  • x³=3x²

<p>nx<sup>n-1</sup></p><ul><li><p>x³=3x²</p></li></ul><p></p>
11
New cards

Constant Rule (derivative of a constant)


0

  • 5=0

  • pi=0

<p><br>0</p><ul><li><p>5=0</p></li><li><p>pi=0</p></li></ul><p></p>
12
New cards

Constant Multiple Rule (cf(x))

cf’(x)

  • 5x4=20x³

<p>cf’(x)</p><ul><li><p>5x<sup>4</sup>=20x³</p></li></ul><p></p>
13
New cards


Sum and Difference Rules (derivative of f(x) ± g(x))


f’(x) ± g’(x)

  • x4+3x2-1 = 4x3+6x

<p><br>f’(x) ± g’(x)</p><ul><li><p>x<sup>4</sup>+3x<sup>2</sup>-1 = 4x<sup>3</sup>+6x</p></li></ul><p></p>
14
New cards

Derivative of sin-1 x

1 / sqrt(1 - x2)

<p>1 / sqrt(1 - x<sup>2</sup>)</p>
15
New cards

Derivative of cos-1 x

-1 / sqrt(1 - x2)

<p>-1 / sqrt(1 - x<sup>2</sup>)</p>
16
New cards

Derivative of tan-1 x

1 / 1 + x2

<p>1 / 1 + x<sup>2</sup></p>
17
New cards

Derivative of cot-1 x

-1 / 1 + x2

<p>-1 / 1 + x<sup>2</sup></p>
18
New cards

Derivative of sec-1 x

1 / |x|*sqrt(x2 - 1)

<p>1 / |x|*sqrt(x<sup>2</sup> - 1)</p>
19
New cards

Derivative of csc-1 x

-1 / |x|*sqrt(x2 - 1)

<p>-1 / |x|*sqrt(x<sup>2</sup> - 1)</p>
20
New cards

Chain Rule f(g(x))

f’(g(x))*g’(x)

<p>f’(g(x))*g’(x)</p>
21
New cards

Derivative of ln x or loge x

1 / x

<p>1 / x</p>
22
New cards

Derivative of loga x

1 / x*ln n

<p>1 / x*ln n</p>
23
New cards

Implicit Rule (dy/dx (x2+y2=25)

2x + 2y*y’ = 0

y’ = -x / y

<p>2x + 2y*y’ = 0</p><p>y’ = -x / y</p>
24
New cards

Expanding Rule (3×2 + 1)2

(3×2 + 1)*(3×2 + 1)

(9×4 + 6×2 + 1)

y’ = 36×3 + 12x

<p>(3×<sup>2</sup> + 1)*(3×<sup>2</sup> + 1)</p><p>(9×<sup>4</sup> + 6×<sup>2</sup> + 1)</p><p>y’ = 36×<sup>3</sup> + 12x</p>
25
New cards

Outside-Inside Rule (3×2 + 1)2

(3×2 + 1)2

y’ = 2(3×2 + 1)*6x

y’ = 36×3 + 12x

<p>(3×<sup>2</sup> + 1)<sup>2</sup></p><p>y’ = 2(3×<sup>2</sup> + 1)*6x</p><p>y’ = 36×<sup>3</sup> + 12x</p>
26
New cards

U - Substitution (3×2 + 1)2

(3×2 + 1)2

y’ = 2u * 6x

y’ = 2(3×2 + 1)2 * 6x

y’ = 36×3 + 12x

<p>(3×<sup>2</sup> + 1)<sup>2</sup></p><p>y’ = 2u * 6x</p><p>y’ = 2(3×<sup>2</sup> + 1)<sup>2 </sup> * 6x</p><p>y’ = 36×<sup>3</sup> + 12x</p>
27
New cards

|x| is equivalent to

Sqrt(x²)

28
New cards

Derivative of ax

ax * lna

29
New cards

Derivaticve of lnex or elnx

x

30
New cards

y = logb x is equivilant to

by = x

31
New cards

y = log10 x is equivilant to

y = log x

32
New cards

y = loge x is equivilant to

y = ln x

33
New cards

When logb(xy)

logb x + logb y or ln x + ln y becauce bm * bn = bm+n

34
New cards

When logb(x/y)

logb x - logb y or ln x - ln y becauce bm/bn = bm-n

35
New cards

When logb xp

P * logb x or P * ln x becauce (bm)n = bm*n

36
New cards

Derivative lny = any function

y*(derivative of that function