Chain Rule :)

polynomial functions

100

The derivative of y = (4x-x²)¹⁰⁰

What is y' = 100(4x-x²)⁹⁹(4-2x)?

200

The derivative of f(x) = (2x+1)⁵⁰⁰

What is f'(x) = 1000(2x+1)⁴⁹⁹?

300

The derivative of F(x) = (x⁴+3x²-2)⁵

What is F'(x) = 5(x⁴+3x²-2)⁴(4x³+6x) or 

F'(x) = 10x(x⁴+3x²-2)⁴(2x²+3)?

400

The derivative of f(x) = (2x-3)⁴(x²+x+1)⁵

What is f'(x) = (2x-3)³(x²+x+1)⁴(28x²-12x-7)?

500

The derivative of h(t) = (t+1)^2/3(2t²-1)³

What is h'(t) = 2/3(t+1)^-1/3(2t²-1)²(20t²+18t-1)?

radical functions

100

The derivative of y = 1/x^1/2

What is y' = -1/2x^-3/2?

200

The derivative of y = (2x)^1/2

What is y' = (2x)^-1/2 or

y' = 1/(2x)^1/2?

300

The derivative of y = (2x)^-1/2

What is y' = -1/2(2x)^-3/2(2) or 

y' = -(2x)^-3/2?

400

The derivative of y = (x²+1)^1/2

What is y' = x/(x²+1)^1/2?

500

The derivative of F(x) = (1-2x)^1/2

What is F'(x) = -1/(1-2x)^1/2?

trig functions

100

The derivative of y = sec(2x)

What is y' = 2sec(2x)tan(2x)?

200

The derivative of y = tan(pix)

What is y' = pisec²(pix)?

300

The derivative of y = (sinx)^1/2

What is y' = cosx/2(sinx)^1/2?

400

The derivative of y = sin(cos(tanx))

What is y' = -cos(cos(tanx))sin(tanx)sec²x?

500

The SECOND derivative of y = cos(x²)

What is y'' = -4x²cos(x²)-2sin(x²)?

surprise :0000

100

Given s(t) = cos(2t), what is v(t)

What is v(t) = -2sin(2t)?

200

Given s(t) = cos(2t), what is a(t)

What is a(t) = -4cos(2t)?

300

DAILY DOUBLE!!

Find the equation of the tangent line to the curve at the given point. 

y = sin(sinx), (pi, 0)

What is y = -x + pi?

400

The position function of a freight train is given by s(t) = 100(t+1)^-2, with s in meters and t in seconds. At time t = 6 s, find the train's VELOCITY

What is -200/343 m/s?

500

DAILY DOUBLE !!!! 

The position function of a freight train is given by s(t) = 100(t+1)^-2, with s in meters and t in seconds. At time t = 6 s, find the train's ACCELERATION

What is 600/2401 m/s²?