AB Calc Flashcards: Plain Trig Derivatives Flashcards

1

Quotient Rule (d/dx (u/v)) =

(u'v - uv')/(uxv)
(uv' + u'v)/v²
(u'v - uv')/v²
(u'v + uv')/v²

2

d/dx tanx =

-sec²x
secx
sec²x
cos²x

3

limit of sinx/x as x approaches 0 is...

cosx
1
0
x

4

PRACTICE: d/dx \frac{x+2}{3x}=

((1)3x - (x+2)(3)) / 3x
((x+2)(3) - (1)3x) / 3x²
((1)3x - (x+2)(3)) / 9x²
((1)3x + (x+2)(3)) / 3x²

5

PRACTICE: d/dx 3x\times\left(\sin x\right)=

3 x cosx
3sinx x 3xcosx
3cosx + 3xsinx
3sinx + 3xcosx

6

Definition of Derivative is...

f'(x) = limit of (f(x+h)-f(x))/h
f'(x) = lim(x->0) of (f(x+h)-f(x))/f(x)
f'(x) = lim(h->0) of (f(x+h)-f(x))/h
f'(x) = lim(h->0) of (f(x)-f(x+h))/h

7

Chain Rule (d/dx (f(g(x))) =

f'(g'(x))g'(x)
f'(g(x))g'(x)
f(g'(x))g(x)
f'(g(x))

8

PRACTICE: d/dx sin(x³) =

3x²sin(x³)
9x²sin(x³)
3x²cos(x³)
9x²cos(x³)

9

PRACTICE: d/dx x⁵ =

25x⁴
5x⁴
4x⁴
x⁴

10

d/dx cotx =

cscx
csc²x
tan²x
-csc²x

11

Alternate Definition of Derivative is...

f'(x) = lim(x->0) of (f(x)-f(a)) / (x-a)
f'(a) = lim(x->a) of (f(a)-f(x)) / (a-x)
f'(x) = lim(x->a) of (f(a)-f(x)) / (a-x)
f'(a) = lim(x->a) of (f(x)-f(a)) / (x-a)

12

d/dx sinx =

-cosx
1
-sinx
cosx

13

Power Rule (d/dx x^n) =

x^(n-1)
nx^(x-1)
nx^(n-1)
(n-1)x^(n-1)

14

Product Rule (d/dx (uv)) =

uv + u'v'
uv x uv
u'v' + u'v'
u'v + uv'

15

d/dx secx =

secx
tan²x
tanx
secxtanx

16

d/dx cscx =

cotx
cscxcotx
-cscxcotx
-cscx

17

d/dx cosx =

sinx
cscx
sin²x
-sinx

AB Calc Flashcards: Plain Trig Derivatives

Questions 17

AB Calc Flashcards: Plain Trig Derivatives

Questions 17