Derivatives

Polynomial

100

6x

6

200

3x²+4

6x

300

7x³-2x

21x²-2

400

3x²(5x)

45x²

500

4x²+5x/8x-6

2(16x²-24x-15)/(8x-6)²

Trig

100

sinx

cosx

200

cos(x)+1

-sinx

300

3tan(2x)+4x

6secx²(2x)+4

400

sinx/e^x

cosx-sinx/e^x

500

cscx(cotx)

-cscx(csc²(x)+cot²(x)

Natural Log

100

ln(x)

1/x

200

ln(2x)

2/2x

300

ln(x²)

(2x)/(x²)

400

Ln(19,999,999,999,999x)

(19,999,999,999,999)/(19,999,999,999,999x)

500

ln(x⁴)

(4x³)/(x⁴)

Log

100

log₅3x²

6x/(3x²)ln5

200

8 Log₅(x)

• (8)/(ln(5)x)

300

log(x²-1)

2x/(x²-1)ln(10)

400

log(5x-x²)

(5-2x)/(5x-x²)ln(10)

500

x²log₅(3x+5)

(3x²)/((3x+5)ln(5))+2xlog₅(3x+5)

Rules

100

d/dx [tanx]=?

sec²x

200

d/dx [ln(u)]=?

u'/u

300

d/dx [logb(U)]=?

u'/uln(b)

400

d/dx [arccot(u)]=?

-u'/1+u²

500

d/dx [arctan(u)]=?

u'/1+u²