Unit 3 Part 2 Jeopardy Review

Chain Rule

100

Find the derivative of 

f(x)=(3x-2x^2)^5

f'(x)=5(3x-2x^2)^4(3-4x)

200

Differentiate: 

y=sqrt(t^2 -2)

y'=t/sqrt(t^2 -2)

300

Find y'. 

y=5cos^2(pit)

y'=-10picos(pit)sin(pit)

400

Differentiate: 

y=sec^2(x)- cot(x^2)

y'=2sec^2(x)tan(x) +2xcsc^2(x^2)

500

Differentiate: 

y=cos^2(1-2x)

y'=4sin(1-2x)cos(1-2x)

Chain Rule #2

100

Find the derivative of 

y=4e^(x^2)

y'=8xe^(x^2)

200

Find the derivative of

f(x)=ln(3x^3)

f'(x)=3/x

300

Differentiate

y=x^3ln(2x)-4x

dy/dx = x^2+3x^2ln(2x)-4

400

Differentiate 

y=(-4x-3)^2(x^5+3)

(-4x-3)(-28x^5-15x^4-24)

500

Find the second derivative of

y=tan(4x)

32tan(4x)sec^2(4x)

Implicit Differentiation

100

Find dy/dx, if

x^2+y^2=25

.

dy/dx=-x/y

200

Find dy/dx. 

x^3 + x^2y + 4y^2=6

dy/dx=(-3x^2 - 2xy)/(x^2 +8y)

300

Find dy/dx. 

sin(x^2y)=5

dy/dx= -2y/x

400

Find dy/dx. 

tan(x-y)=y

dy/dx=[sec^2(x-y)]/[sec^2(x-y)+1]

500

Find the second derivative for the following

5y^2+4=2x^3

(d^2y)/(dx^2)=(30xy^2-9y^4)/(25y^3)

Related Rates

100

Find dy/dt when y=x^3, x=4, and dx/dt=3

dy/dt=144

200

The radius r of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change of the area when r=6 centimeters.

60∏ squared centimeters per minute

300

All edges of a cube are expanding at a rate of 2 centimeters per minute How fast is the volume changing when each edge is 10 centimeters?

600 cubed centimeters per minute

400

Air is being pumped into spherical balloon at a rate of 50 cubic feet per minute. At what rate is the radius changing when the radius is 8 feet?

25/128∏ feet per minute

500

A ladder 10 feet long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall?

-.75 feet per second

Miscellaneous

100

Find the Derivative of 

y=sin(ln(x))

y'=cos(ln(x))/x

200

Find g'(t).

g(t)=1/(sin(2t)+4)

g'(t)=-(2cos(2t))/(sin(2t)+4)^2

300

Find dy/dx, then evaluate the derivative at the point (1,0):

x^2y + xy^2=3x

dy/dx=[3-2xy-(y^2)]/[(x^2)+2xy]

 

dy/dx=3

400

Where did Mrs. Henderson work during the summer in high school?

Hershey Park

500

The length of a rectangle is decreasing by 7 in/sec and the width is shrinking at 3 in/sec. Find the rate of change of the area at the instant when the length is 4 inches and the widths is 8 inches.

-68 in²/sec