Derive It

lnx,e^x,a^x

100

d/dx[e^x]=?

e^x

200

What happens when ln/e?

It cancels

300

e^-infinity

0

400

a^m/aⁿ can also be written as?

a^m-aⁿ

500

d/dx[ln(x²+2)]=?

2x/x²+2

Quotient Rule

100

x²/e^x

(2xe^x-x²e^x)/(e^x)²

200

Cos(x)/Tan(x)

[-Sin(x)Tan(x)-Cos(x)Sec²(x)]/Tan²(x)

300

Sin(x)/Csc(x)

[Cos(x)Csc(x)-Sin(x)(-Csc(x)(Cot(x))]/(Csc²x)

400

Cot(x)/ln(x)

(-Csc²xlnx)-(Cot/x)/(lnx)²

500

Arccos(x)/Tan(x)

[(-1/sqrrt(1-x²))Tan(x)-(arccos(x)Sec²(x)]/Tan²(x)

Product Rule

100

Cos(x)Sin(x)

-Sin(x)Sin(x)+Cos(x)Cos(x)

-Sin(x)Sin(x)+Cos²(x)

200

Tan(x)Sin(x)

Sec²(x)Sin(x)+Tan(x)Cos(x)

300

Tan(x)Sec(x)

Sec²(x)Sec(x)+Tan(x)Sec(x)Tan(x)

or 

Sec³(x)+Tan²(x)Sec(x)

400

Write the formula for product rule

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

500

Arctan(x)Sin(x)

[Sin(x)+Arctan(x)Cos(x)]/1+x²

Chain Rule

100

Cos(x³)

-3x²sin(x³)

200

Csc(lnx)

[-csc(lnx)cot(lnx)]*1/x

300

Tan(x²-2)

2xSec²(x²-2)

400

Write the chain rule formula

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

500

Arccsc(x²)

-2x/|x²|rt(x⁴-1)

Power Rule

100

X⁵

5x⁴

200

3x²

6x

300

1/x

-1/x²

400

1/5x²

-1/10x

500

Write the power rule formula 

nx^n-1