CALC review - formulas + rules

Trig Rules

100

cos x

-sin x 

200

tan x 

sec² x

300

cot x

-csc² x

400

sec x 

sec x tan x

500

csc x 

-csc x cot x

Chain Rule

100

sin (3x²+2x)

cos(3x²+2x) * (6x+2)

200

e^{5x^3-2x}

e^{5x^3-2x} * (15x²-2)

300

ln(4x²+3x+1)

8x+3 / 4x²+3x+1

400

cos(2x²-3x)

-sin(2x²-3x) * (4x-3)

500

(3x²-4x+1)⁵

5(3x²-4x+1)⁴ * (6x-4)

Quotient Rule

100

What is the Quotient Rule?

dy/dx = [v (dy/dx) - u (dy/dx)] / v²

200

x²+3x / x³-2x

-x⁴-6x³-2x² / (x³-2x)²

300

3x²-5 / x+2

3x²+12x+5 / (x+2)²

400

5x³+4x / 2x²-3x

10x⁴-30x³-8x² / (2x²-3x)²

500

2x³-4x / x²+1

2x⁴+10x²-4 / (x²+1)²

Product Rule

100

What is the Product Rule?

u(dv/dx) + v (du/dx)

200

(2x³-4x)(x²+1)

10x⁴-6x²-4

300

(x²+1)(x³-3x)

5x⁴-6x²-3

400

(x⁴+2x)(x²-3x+4)

6x⁵-15x⁴+16x³+6x²-12x+8

500

(x²-1)(sin(x))

2x sin (x) + (x²-1)cos(x)

Special

100

Definition of Derivitive?

lim      f(x+h)-f(x)/h

h->0

200

L'Hopital's Rule?

lim    f(x) / g(x)  = lim    f'(x) / g'(x)

x->c                     x->c

300

Power Rule?

nx^n-1

400

Square Root Rules

cos x

500

Log and Exponential Rules?

ln (x)' = 1/x

log_a(x)' = 1/ x ln a

e^{x '}= e^x

x^x=x^x (1+ln x)