October 1st SI

C8-Chain

100

f(x) = (2x+1)²

Find f'(x)

2(2x+1) • 2 

OR

 4(2x+1)

OR

8x+4

200

f(x) = 1 / (x²+9x)²

Find f'(x)

-2(2x+9) / (x²+9x)³

This was the in class example on 10/01/25!

300

f(x) = (sin(x))² + 3x

Find f'(x)

2(sin(x))+cos(x)+3

400

f(x) = (3x³-2x+5x²-3) ^ (2/3)

2(9x²+10x-2) / 3(3x³ + 5x² -2x -3)

500

f(x) = ((x³+2x²+5x-3) ^(3/2)) / ((3x+2)^2)

(3x+2)²•(3/2)•(√(x³+2x²+5x-3)•(3x²+4x+5) + ((x³+2x²+5x-3)^(3/2) )•(2)•(3x+2)•(3)

C7 -ProductQuotient

100

h(x) = (x²-4)(3x+2)

Find h'(x)

(3x+2)(2x)+(x²-4)(3) 

OR

9x²+4x-12

200

h(x) = (x⁴+2x²-1) / (3x²-4x+1)

Find h'(x)

((3x²-4x+1)(4x³+4x) - (x⁴+2x²-1)(6x-4) ) / (3x²-4x+1)²

300

h(x) = sin(x) / cos(x)

Find h'(x)

sec²x

400

h(x) = (x²-2x+3)² • (3x+2)³

Find h'(x)

(3x²+2)³•(2(x²-2x+3)(2x-2)) + (x²-2x+3)²•(3(3x+2)²(3))

500

h(x) = (x²+3x-1)⁵ / (x³+6x+2)³

Find h'(x)

(  (x³+6x+2)³ * 5(x²+3x-1)⁴*(2x+3) - (x²+3x-1)⁵ *3(x³+6x+2)²*(3x²+6)  ) / (x³+6x+2)⁶

C6-BasicDerivatives

100

f(x) = 3x

find f'(x)

3

200

f(x) = sin(x)

Find f'(x)

cos(x)

300

f(x) = cos(x)

Find f'(x)

-sin(x)

400

f(x) = tan(x)

f'(x)

sec²(x)

500

f(x) = sec(x)

f'(x)

sec(x)tan(x)

S2-Indeterminate forms

100

Limit of f(x) as x approaches 3

f(x) = (x²-6x+9) / (x-3)

0

200

Limit of f(x) as x approaches 4

f(x) = (x²-16)/(x-4)

8

300

Limit of f(x) as x approaches 2

f(x) = x-2/x²-4

1/4

400

Limit of f(x) as x approaches 3

f(x) = (x²-3x) / (√(x+6) -3)

18

500

Limit of f(x) as x approaches 0

f(x) = (x³+4x²+5x-10) / (x-1)

16

Harder Questions, mixed

100

h(x) = (sin(x) + cos(x))² / (3x³-4x+2x²-1)

h'(x)

((3x³-4x+2x²-1)(2)(cos²(x)-sin²(x)) - (9x²-4+4x)(sin(x)+cos(x))²) / (3x³-4x+2x²-1)²

200

h(x)= sin(x)cos(x)

Find h'(x)

-sin²x + cos²x

300

As x approaches 0 of f(x), f(x) approaches what number

f(x) = -1/|x|

Negative infinity

400

f(x) = tan(x)cos(x)

Find f'(x)

f'(x) = cos(x)

500

f(x) = e^5sinx

f'(x)

f''(x)

f'(x) = 5cosx*e^5sinx

f''(x) = -5sin(x)*e^5sinx + 25cos²(x)*e^5sinx