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Logs

100

ln57

1/57

200

log₄(31)

1/ln(4)31

300

ln4+log₅(43)

1/4+1/ln(5)43

400

log₄₆(54)

1/ln(46)54

500

ln4222245466555655

1/4222245466555655

Matrix

100

4x³  7

65x  5  

12x²  0

65    0

200

-7x³   6x^-5

33    4x⁴

-21x²   -30x^-6

0       16x³

300

10x⁷   5x^-4   8x³

-4x¹⁰  44x    39

3x     4x¹²    20x^-2

70x⁶  -20x^-5  24x²

-40x⁹  44     0

3        48x¹¹  -40x^-3

400

46x²    67x⁴

378x   -24x^-7

92x   268x³

378   168x^-8

500

12x^-20 44x⁵  89x²

34x   22x^-11  -49

-3x²⁶  57x    -33x^-5

-240x^-21  220x⁴  178x

34   -242x^-12    0

-78x²⁵  57   165x^-6

Power rule

100

f(x)=−3x2 +4

-6x

200

−4x²−5x−2

-8x-5

300

5x¹⁸

90¹⁷

400

2x^2/3

4/3x^-1/3

500

−3r⁵−5r²+45r⁵-23+13r^1/3

-15r⁴-10r+225r⁴13/3r^-2/3

Product

100

(x+2x³)(4x)

(1+6x²)(4x)+(x+2x³)(4)

200

x²(−3x² −2)

2x⋅(−3x² −2)+x²⋅-6x

300

(-2x⁴-3)(-2x²+1)

(-8x³)(-2x²+1)+(-2x⁴-3)(-4x)

400

(5x⁵+5)(-2x⁵-3)

(25x⁴)(-2x⁵-3)+(5x⁵+5)(-10x²)

500

(-2x⁴+5x²+4)(-3x²-4)

(-8x³+10x)(-3x²-4)+(-2x⁴+5x²+4)(-6x)

Quotient rule

100

3x²/x⁵

(6x)(x⁵)-(3x²)(5x⁴)/x¹⁰

200

2x^-4/5x²

(-8x^-5)(5x²)-(2x^-4)(10x)/25x⁴

300

4x¹²/-3x⁹

(48x¹¹)(-3x⁹)-(4x¹²)(-27x⁸)/9x¹⁸

400

24x⁵/8x²⁰

(120x⁴)(8x²⁰)-(24x⁵)(-160x²¹)/64x⁴⁰

500

33x⁴/-21x⁴⁴

(132x³)(-21x⁴⁴)-(33x⁴)(-924x⁴³)/441x⁸⁸