Calculus Review Game- Finding Derivatives

Basic Derivative Information and Power Rule

100

The derivative calculates the ________.

Slope

200

d/dx 5 =

0

300

d/dx x² =

2x

400

d/dx 3x²-x+3 =

6x-1

500

What does the Intermediate Value Theorem state?

If f(x) is continuous on the interval [a,b], then there exists a c in the interval such that f(a) < f(c)< f(b).

Chain Rule

100

Define the Chain Rule for f(g(x))

g′(x)f′(g(x))

200

d/dx (e^{7x^2})

14xe^{7x^2}

300

d/dx sin(4x²)

8xcos(4x²)

400

Differentiate y = √(13x²-5x+8)

y′ =(26x-5)/ (2√(13x²-5x+8))

500

Differentiate y=3tan(√x)

y′ =3sec²(√x)/ 2√x

Product Rule

100

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

f′(x)g(x)+ g′(x)f(x)

200

f(x)=x²sinx, what is f′(x)?

2xsinx+ x²cosx

300

Differentiate y=x³lnx

y′ =x²(1+3lnx)

400

Differentiate y=e^-x²cos2x

y′ =−2xe^(−x²) cos2x−2e^(−x²)sin2x

500

Differentiate y=x²sin³(5x)

y′ =xsin²(5x)[15xcos(5x)+2sin(5x)]

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+lnx) / (x²-lnx)

y′= [(1/x)-x-2xlnx] / (x²-lnx)²

400

f(x)= (x²-1)³/ x²+1, what is f′(x)?

f′(x)= [4x(x²-1)²(x²+2)] / (x²+1)²

500

Differentiate y= (x³lnx)/(x+2)

y′ = [x²(2xlnx+6lnx+x+2)]/ (x+2)²

Trig Derivatives +Chain Rule

100

d/dx cos(2x)=

-2sin(2x)

200

Differentiate y=tan³(x)

y′ =3tan²(x)sec²(x)

300

Differentiate y=csc(cos(x))

y′ =csc(cos(x))cot(cos(x))sin(x)

400

d/dx sin(e^7x)

7e^7xcos(e^7x)

500

d/dx arcsec(5x)=

5/ |x| √(x² - 1)