Derivatives!

Trig

100

 1/Cos(x)?

Sec(x)

200

sin²(x) + Cos²(x)=

What is 1

300

d/dx [sin(kx)]=

What is kcos(kx)?

400

d/dx[3tan(2x) +1]

What is 6sec²(2x)

500

The derivative of f(x)= -5sec(6x)

What is -30sec(6x)tan(6x)

Product Rule

100

d/dx[xe^x]=

In its simplest form:

What is e^x(1+x)

200

Derivative of h(x)= f(x)g(x)

What is h'(x)= f'(x)g(x) + f(x)g'(x)

300

I want to Rephrase 1/x² so I can differentiate without quotient rule. How?

What is (x)^-2

400

How do I differentiate 2x²+ x³Sinx

What is 4x + [x³(Cosx) + 3x²(Sinx)]

500

What is f'' of 2(x²-4)(x³+2x+2)?

What is f''= 40x³-24x+8

Quotient Rule

100

Derive: x/x2

What is -1/x²

200

Spot the error:

d/dx[f(x)g(x)]= (g'(x)f(x)-g(x)f'(x) ) / g(x)

What is:

d/dx[f(x)g(x)]= (g(x)f'(x)-g'(x)f(x) ) / (g(x))²

300

Solve:

d/dx[(5x+1)/(3x-4)]

-23/(3x-4)²

400

What is the f(x) function in d/dx[(5x+1)/(3x-4)]?

What is (5x+1)

500

What is the f(x) function in d/dx[(5x+1)/(3x-4)]?

What is (3x-4)

Random

100

What's the Linearization formula?

What is L(x)= f(a) + f'(a)(x-a)?

200

Using the table provided, state 2*p'(2) if p=f(g(x))

What is 126?

300

what is y' if y=(log2x)^3

What is 3(log2x)^2 * 1/(xln2)

400

What's hi in spanish?

What is Hola

500

Using logarithmetic diff. what is dy/dx if y=(secx)^x

What is dy/dx= (ln(secx) + xtanx) (secx)^x

Chain Rule

100

State chain rule if h(x) = f (g(x)) 

What is h'(x)= f'(g(x)) * g'(x)

200

What is the most outside function of h(x)= Sin(tan(1+x))

What is Sin(x)

300

What is the derivative of y = e^{x^2}cos(x²)

WHat is y'= 2xe^{x^2}cos(x²) + e^{x^2}(−2x sin(x²))

400

What rule(s) would you use to differentiate f(x)=(tan²x)(secx)

What is product and chain rule

500

WHat is the derivative of f(x)=(tan²x)(secx)

What is 2tanx(sec²x)(secx) + tan²x(secxtanx)