Math 151A JEOPARDY Final review

Derivatives

100

Differentiate (6x²+7x)⁴

4(12x+7)(6x²+7x)³

200

Differentiate 6x²/(2-x) (make sure to simplify it!)

24x - 6x²/(2-x)²

300

Differentiate f(x) = 2cosx - 6secx + 3

-2sinx - 6secxtanx

Limits

100

Lim_x->2 (x²+4x-12) / (x²-2x)

4

200

lim_x->2(8 - 3x + 12x²)

50

300

Lim_x->0 x/(3-sqroot(x+9))

-6

Implicit Differentiation

100

2x³=(3xy+1)²

(-3y²x-y+x²)/(3x²y+x)

200

3x²y²=4x²-4xy

(4x-2y-3xy²)/(3x²y+2x)

300

tan(x²y⁴) = 3x + y²

3-2xy⁴sec²(x²y⁴) / 4x²y³sec²(x²y⁴)-2y

Log/exponential Differentiation

100

Differentiate 2e^x - 8^x

2e^x - 8^xln8

200

Differentiate y = z⁵ - e^zlnz

5z⁴- e^zlnz - e^z/z

300

lim_t->0 (8^t-5^t)/t

ln(8/5) or ln8 - ln5

Anti-derivatives

100

Find the antiderivative of y = x⁴ + 3x² - 9x + 9

x⁵/5 + x³ - 9x²/2 + 9x + C 

200

Evaluate the integral 6x⁵-18x²+7 dx 

x⁶ - 6x³+7x + C

300

integrate: cuberoot(w) + 10w^3/5dw 

3/4w^4/3+25/4w^8/5+C