MATEEEE

Product Rule

100

Solve:

(1+8x2)(x-x2)=

-32x3+24x2-2x+1

200

Solve:

3x lnx

 3lnx+3

300

Solve:

4e3xcosx=

-4e3xsinx+12e3xcosx

400

Solve:

(4x6-7x2+3)(6x5+2x3)=

264x10+72x8-294x6+20x4+18x2

500

Solve:

x7sin(3x+2x2)=

x7cos(3x+2x2)(3+4x)+7x6sin(3x+2x2)

Quotient

100

Solve:

36x/x²+36=

-36x²+1296/(x²+36)²

200

Solve:

3-6x/7-4x=

-30/(7-4x)²

300

Solve:

4x(1 -6/x+7)=

4x²+56x+28/(x+7)²

400

2-2x-x²/x²-5=

2x²+6x+10/(x²-5)²

500

6x-11x/root of X

6x+11/2x^3/2

Rules of Log

100

(Lnu)'=?

u'/u

200

(log_au)'=?

u'/(lna)u

300

log₅(6x+4/2x-3)=?

log₅(6x+4)-log₅(2x-3)

400

5x+6ln(3x+1)=

18/3x+1 (+5x)

500

8ln Root of 2x+4=

8/2x+4

Chain Rule

100

y=(x²-6)³

6x (x²-6)²

200

y=5/(3x²-1)²

  -60x(3x²-2x+1)³

300

y=ln Root of x²+8

x/x²+ 8

400

y=sin 4x/ 1+ cos 4x

 4/1+ cos 4x

500

log₆(tan7t²)

14tsec²7t²/ln6tan7t²

Trigonometrics

100

CSC²(x)=

-2 cot(x)csc²(x)

200

cos(x)cot(x)=

-cos(x)-cot(x)csc(x)

300

cos(x²-x)=

-(2x-1)sin(x²-x)

400

10 tan(x)-2cot(x)

2(csc²(x)+5sec²(x))

500

(tan(x)/2+e^x)²

1/2(2e^x+tan(x))(2e^x+sec²(x))