Product Rule

Vocabulary

100

There are two multiplied against each other which makes you use the product rule to find the derivative

What is a function

200

Rate of Change

What is a derivative

300

What is another word for derivative that is a straight line just touching a point of a function

What is tangent

400

What is used to find the derivative of two functions multiplied against each other?

What is the product rule

500

What is the product rule

What is y' = f '(x)*g(x) + g '(x)*f(x)

Polynomial Problems

100

f(x)=(3x²)(-5x)

f '(x)=-45x²

200

d/dx((-2x³-3x-6)(-x²))

dy/dx=10x⁴+9x²+12x

300

y =(2x⁴+7x-6)(-2x³+6)

y'=-28x⁶-8x³+36x²+42

400

d/dx (((2/3)x^-2)(5x⁴+(1/2)x^-1))

dy/dx = (20x³-(1/2)x^-2)((2/3)x^-2)+(5x⁴+(1/2)x^-1)((-4/3)x^-3)

500

f(x)=(x^1/3+x^-1/4)(6x²-1)

f '(x)=(3x^-2/3-4x^-5/4)(6x²1)+12x(x^1/3+x^-1/4)

Trig Problems

100

f(x)=sin(x)cos(x)

f '(x)=sin(x)(-sin(x)+cos(x)*cos(x)

f '(x)=-sin²(x)+cos²(x)

200

f(x)=sin(x)(-2x⁶)

f '(x)=−12x⁵(sin(x))+(-2x⁶)(cos(x))

300

y=cot(x)sin(x)

dy/dx=cos(x)cot(x)-csc²(x)sin(x)

400

y=-3sin(x)csc(x)

dy/dx=3cot(x)csc(x)sin(x)-3cos(x)csc(x)

500

d/dx((4tan(x)+3x²)(-sin(x)-1)

dy/dx=(4sec²(x)+6x)(-sin(x)-1)-cos(x)(4tan(x)+3x²)

Symbols/Misc.

100

f(x)

what is a function

200

What is the best math subject?

What is calculus?

300

f '(x)

what is derivative 

400

True or False: All the derivative rules can be used in each other.

What is true

500

d/dx

what is derivative