Calculus Jeopardy! (Derivatives)

D' Rules Are Simple

100

Generally speaking, my derivative is always zero

What is a constant?

200

d/dx x^n

n*x^(n-1)

300

My nickname is "left, d-right, plus right, d-left"

What is the product rule?

400

d/dx f(g(x))

f'(g(x))*g'(x)

500

d/dx (f(x)/g(x))

(g(x)*f'(x)-f(x)*g'(x))/(g(x))^2

Poly-wanna-nomial

100

If y=x then I am y'

What is 1?

200

d/dx 1738x

1738

300

d/dx (5x^2+2x-3)

can be broken up this way

d/dx 5x^2 +d/dx 2x-d/dx 3

400

d/dx (24x^3+17x^2-98x+237)

72x^2+34x-98

500

d/dx ((x^2+3)(x-4))

in expanded polynomial form

3x^2-8x+3

TranscendentalThoughts

100

This function is exactly equal to its derivative

What is 

e^x

200

The derivative of this function is 

1/x

What is 

ln(x)

300

d/dx 5^x

5^x ln(5)

400

d/dx log_a(x)

1/(x*ln(a)

500

d/dx log_2(ln(x))

1/(ln(x)*ln(2))*1/x

Gettin' Triggy with It

100

d/dx sin(x)

cos(x)

200

d/dx sec(x)

sec(x)tan(x)

300

The derivative of this function is equal to the reciprocal of its denominator squared

\text{What is }\tan(x)?

400

d/dx cos^-1(x^2)

{-2x}/sqrt(1-x^4)

500

d/dx sec^-1(e^(2x+5))

{2e^(2x+5)}/(abs(e^(2x+5))sqrt((e^(4x+10))-1))

Going Off On A Tangent

100

f(x)=2x+5

at x=3

y-11=2(x-3)

200

y=x*e^x-e^x

at (1,0)

y=e(x-1)

300

y=csc^-1(sqrtx)

at x=2

y-\frac{\pi}{4}=-1/4(x-2)

400

f(x)=log_5(x^3)

at x=5

y-3=(3/(5ln(5)))(x-5)

500

y=(e^x/cos(x))

\text{at } x=pi

y+e^{\pi}=-e^(\pi)(x-pi)