Ch.2 Review Game- The Derivative

Basic Derivative Information and Power Rule

100

The derivative calculates the ________.

Slope

200

d/dx -5x⁴ = ?

-20x³

300

d/dx x²+4x³-10 =

2x+12x²

400

d/dx 3x²-x+3 =

6x-1

500

Speed is _________.

the absolute value of velocity

Random Qs

100

Find y'' of:  x - e^x

-e^x

200

Find equation of tangent line: 

f(x)=x²+4x-3 ;  x= -5

y=-6x-28

300

What is the instantaneous velocity at the given time?s(t)=(3t²-1)/t   at time t=1 seconds  (s is in cm)

7 cm/sec

400

When does a particle change direction?

v(t)=0 and there's a change of sign!

500

Find the derivative of the function at the given number.

f(x)=x^1/2  ;  at x=4

1/4

Product Rule

100

Define the Product Rule using f(x)g(x)

f′(x)g(x)+ g′(x)f(x)

200

f(x)=x²e^x, what is f′(x)?

xe^x(x+2)

300

Differentiate y=x²(x³-1)

y′ =5x⁴-2x

400

Differentiate y=(3x²-5)(2x+1)

y′ =18x²+6x-10

500

Find y'' of f(x)=xe^x

y′'=e^x(2+x)

Quotient Rule

100

Define the Quotient Rule using f(x)/g(x)

[g(x)f′(x) - f(x)g′(x)]/ (g(x))²

200

Differentiate y= 2/(x+1)

y′ = -2/ (x+1)²

300

Differentiate y= (1-2x) / (1+2x)

y′= -4 / (1+2x)²

400

find the equation of tangent line at point:

f(x)=x³/(x+1)  at (1, 0.5)

y= 5/4x-3/4

500

Differentiate y= e^x/x²

y′ = e^x(x-2)/x³

Trig Derivatives

100

d/dx cosx=

-sinx

200

Differentiate y=tan(x)

y′ =sec²(x)

300

Differentiate: y=tanx + cos x

y′ =sec²x-sinx

400

Differentiate:  y=tcost

y'=cost - tsint 

500

Find the derivative of: 

y=sinx/e^x

y'=(cosx-sinx)/e^x