The Calculus Jeopardy @ PCI - Part IV

Chains of Love

100

The derivative of
f(x) = sqrt(984+x^2 

x/sqrt(984+x^2)

200

The derivative of
f(x) = e^(3x^4) 

12x^3(e^(3x^4))

300

The derivative of  
f(x) = pi^(x^2) 

 2xpi^(x^2)ln(pi) 

400

The derivative of
f(x) =  ln (x-x^3) 

 (1-3x^2)/(x-x^3 

500

The derivative of
f(x) =  sqrt(ln x) +1 

1/(2xsqrtlnx)

In-TRIG-uing

100

The derivative of
f(t) = sin 5t

5cos 5t

200

The derivative of
f(t) =  cos 3t 

-3sin 3t

300

The derivative of
f(t) =  -1/2tan t^2 

-tsec^2(t^2)

400

The derivative of
f(t) =  cos^2 (t) 

-2cos(t)sin(t)

500

The derivative of
f(x) =  sqrt sec(t) 

(tan tsect)/(2sqrtsect) or 1/2tan tsec^2t

Expo

100

The value of a in  sqrt(x^(7)) =x^a 

7/2

200

The value of a in 27 = 3^a 

3

300

The value of a in x^4sqrtx=x^a 

9/2

400

The value of a in sqrtx/x^3 = x^a 

-5/2

500

The value of a in 8x^3=(sqrt(2x))^a 

6

Antiderivatives

100

 int1/xdx 

lnx+c

200

 int(sqrtx) dx 

(2/3)x^(3/2)+c

300

 intcos(x) dx 

sin(x)+c

400

 intx^2+2x dx 

(x^3)/3+x^2+c

500

 int-sin(x)dx 

 cos(x) + c  

Integrals

100

 int8x+x^3dx 

4x^2+x^4/4+c

200

 int2/(5x)dx 

2/5lnx+c

300

 intsqrtx+ 4xdx 

2/3x^(3/2)+ 2x^2c

400

 int75.38dx 

75.38x +c

500

 int(x+16)^16dx 

(x+16)^17/17+ c