Derivative Rules

Trig functions

100

Given: f(x)=tan(x) Find: f'(x)

sec²(x)

200

Derivative of secant

sec(x)tan(x)

300

f(x)= x²+sin(x) f'(x)=

f'(x)=2x+cos(x)

400

f(x)=sin(x)cos(x)    f'(x)=

f'(x)=cos²(x)-sin²(x)

or

f'(x)=-sin²(x)+cos²(x)

500

What is USA national Flower?

Rose

random derivatives

100

Apply differentiation rules to determine the derivative of the function: y = sqrt(x)-cuberoot(x²)

1/(2 sqrt(x))- 2/(3cuberoot(x))

200

f(x) = 7x³ - 3x^-2 f'(1)=

18

300

Determine the slope of a line normal to the tangent line at x = -1. f(x) = -(x+7x²)

-1/13

400

Determine the equation of a line that is normal to the tangent line at x = -1. f(x) = (2x^-1 - 7)²

y = -1/36x + 2915/36

500

What year did Mrs. M graduate from college?

2005

Power Rule

100

Determine f'(x) for: f(x) = 5

0

200

f(x) = 4x⁴ − 5x − 3

f '(x) = 16x³− 5

300

f(x)=3/x³    f'(x)=

f'(x)= -9/x⁴

400

Random Question!!!!!

f = - 1 / t²

2t^-3

500

what is the only food that never spoils?

Honey

Quotient Rule

100

f(x) = 2/(2x⁴-5)

-16x³/(2x⁴-5)²

200

(3x⁴+2)/(3x³-2)

(12x³(3x³-2)-9x²(3x⁴+2))/(3x³-2)²

300

 y = (x+1)/(x² + 4x + 1) 

(x²+4x+1-(x+1)(2x+4))/(x²+4x+1)²

400

Random question

4/x²

-8x^-3

500

What animal is known to laugh and has been proven to have a sense of humor?

Rat

Product Rule

100

-x³(3x⁴-2)

-21x⁶+6x²

200

Determine f'(x): f(x) = (5x⁵+5)(-2x⁵-3)

get the simplest form!

-100x⁹-125x⁴

300

Differentiate f(x) = x³(2 - 5x³)

simplest form!

6x²-15x⁵-15x⁴

400

Determine the slope of the tangent when x = 1: y = cos(x)(1 + x²)

-sin(x)(1+x²)+cos(x)(2x)

500

In which year did World War II end?

1945