Unit 2B

Derivatives of Trig Functions Pt 1

100

the derivative of ln(x⁶)

6/x

200

the derivative of sin(4x⁵)

20x⁴cos(4x⁵)

300

the derivative of e^{5x^2}

5xe^{3x^2}

400

the tangent line to f(x)=tan(x)+9cos(x) at x = π (pi)

y=x−π−9

500

the slope of the line tangent to the graph y = ln(x) + e^2x at x = 2

1/2 + 2e⁴

Derivatives of Trig Functions Pt 2

100

The derivative of cotx

What is csc²x

200

The derivative of secx at x = pi / 2

What is DNE

300

The derivative of 5xcsc²x

What is 5csc²x - 10xcsc²xcotx

400

The derivative of x³tan4x at x = pi / 3

What is 3x²tan4x + 4x³sec²4x

500

The derivative of cotx / tanx at x = pi/3

What is -8/9

Product Rule

100

What is the formula for The Product Rule?

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

200

y = sin(x)cos(x)

y' = cos²x - sin²x

300

y = x²ln(x)

y' = 2xln(x) + x

400

y = x³e^2x

y' = 3x²e^2x + 2x³e^2x

500

y = e^3xsin(3x)

y' = 3e^3xsin(3x) + 3e^3xcos(3x)

Quotient Rule

100

The derivative of the function: f(x)= x²+3/e^x

f′(x)= −x²+2x−3/e^x

200

 The derivative of the function: g(x)= sin⁡(x)/x²+1
(you can leave this one non-foiled). 

g′(x)= cos(x)(x²+1)−2xsin(x)/(x²+1)²

300

The derivative of the function: h(x)= x⁵/x³+x
(factor the solution).

h′(x)= 2x⁵(x²+2)/(x³+x)²

400

Find the derivative of the function: k(x)= ln(x)/x²

k′(x)=1−2ln(x)/x³

500

Differentiate the function: m(x)= x⁴+1/sin(x)

m′(x)= 4x³sin(x)−(x⁴+1)cos(x)/sin²(x)