Derivative Jeopardy

Column 1

100

Find the derivative (what rule(s) were used): y=15x⁴

dy/dx=60x³

Rule(s): Power Rule

200

Find the Tangent Line (list steps): y=x²+1 (1,1)

y-1=2(x-1) or y=2x-1

1. Find the derivative of the given equation

2. Plug in x value to obtain slope

3. Plug in given values and slope into slope formula (answer)

300

Which trig functions result in a negative derivative?

y=cos(x)

y=csc(x)

y=cot(x)

400

Differentiate and Identify if it is a Double or Single Chain: y=(sin(5x))²

dy/dx=10sin(5x)cos(5x)

-Double Chain Rule

u=sin(5x)

du=5cos(5x)

500

Differentiate and List All Rule(s) Used: y=sec(2x⁵/(2x⁴+5)

dy/dx=2x⁴sec(2x⁵/(2x⁴+5))tan(2x⁵/(2x⁴+5))(2x⁴+25)/(2x⁴+5)²

Rule(s): Chain Rule, Power Rule(may not count), and Quotient Rule

Column 2

100

Which derivative rule does this represent? dy/dx= f(g(x))

The Chain Rule (Derivative of a composite function)

200

Which trig function(s) result in a derivative that includes the absolute value of itself as part? Respond with the trig function(s) and its derivative.

y=sec(x); dy/dx=sec(x)tan(x)

y=csc(x);dy/dx=-csc(x)cot(x)

300

Find the Derivative of this Function: y= -4x²(5x³-1)

dy/dx= -100x⁴+8x

Aside: u= -4x², du= -8x, v=5x³-1, dv=15x²

Then use Product Rule (uv'+vu') and plug in the aside values to evaluate.

400

Describe 1 ways the product and quotient rules are similar and 1 way they are different

(Answers may vary):

1. "u" and "v" components of a product rule derivative are interchangeable whilst "u" and "v" components of a quotient rule derivative are not interchangeable. (difference)

2. An aside can be used to organize components of the product or quotient. (similarity)

500

If a function is non differentiable at a certain point, then does the derivative exist at that point?

No, the derivative would not exist (think of a corner or spike; the slope at that point will differ depending on how you look at. Thus, there isn't a derivative.)

Column 3

100

What do the u and v represent in the quotient rule?

u is the numerator and v is the denominator of the function being differentiated

200

What is the derivative rule of e^x?

dy/dx(e^x)=x'e^x or dy/dx(e^u)= u'e^u

300

If the exponent is higher than the base of a logarithmic, what kind of function is its derivative?

A rational function.

For example: y= ln(3x⁴); y'=4/x

400

Describe the derivative of y=e^{5x^7}:

The derivative of this function is itself multiplied by the derivative of the exponent (5x⁷)

y'=35x⁶e^{5x^7}

500

Describe 3 trends of trig derivatives.

(Answers may vary):

1. y=csc(x) and y=sec(x) contain the absolute value of themselves in their derivative.

2. All trig functions that start with c have a negative derivative.

3. The derivative of y=sin(x) and y=cos(x) result in the absolute value of the other function as their derivative.