Calculus Derivatives Review!

Derivative Rules

100

The derivative calculates the _______.

slope

200

d/dx (15) = 

0

300

d/dx Ax = 

 A

400

d/dx (ax² + bx + c) = 

What is 2ax + b

500

The derivative of an object's position with respect to time is it's _________.

velocity

Product Rule

100

Define the Product Rule using f(x)g(x)

What is: f'(x)g(x)+g'(x)f(x)

200

If y = x³(lnx), dy/dx = 

dy/dx = 3x²(lnx) + x³(1/x)

300

If y = x³(2x²+5x+3), dy/dx = 

What is dy/dx = 3x²(2x²+5x+3) + x³(4x+5)

400

What is the derivative of f(x) = (3x²+5x³)e^5x

What is f'(x) = (6x+15x²)e^5x+(3x²+5x³)5e^5x

500

d/dx (4sect+tant), Simplify fully!

sect(4tant+sect)

Chain Rule

100

Define the Chain Rule as f(g(x))

What is f'(g(x))*g'(x)

200

What is the derivative of f(x) = (-4x+3)². Simplify fully!

What is f'(x) = 32x-24

300

If y = ln((5x²+3x), dy/dx = 

What is dy/dx = (1/(5x²+3x))(10x + 3)

400

The derivative of f(x) = (ln(x)+3x²+e^x)⁴

What is f'(x) = 4(ln(x)+3x²+e^x)³(1/x + 6x + e^x)

500

If f(x) = _ee^x(x+5) . f'(x) = 

f'(x) = _ee^x(x+5)(e^x(x+5))((x+5)+x)

Quotient Rule

100

Define the Quotient Rule as f(x) = u/v

What is (vdu - udv)/(v²)

200

If y = (x⁵-5x²)/(x+2), dy/dx = 

What is dy/dx = ((x+2)(x⁵-5x²) - (5x⁴-10x))/((x+2)²)

300

If y = (x³+5x)/(2x⁵-7), dy/dx = 

((2x⁵-7)(3x²+5)-(x³+5x)(10x⁴))/((2x⁵-7)²)

400

If y = 3x²/e^x, dy/dx = 

dy/dx = (e^x(6x)-3x²e^x)/(e^2x)

500

The derivative of f(t) = e^-5t/(t^-5+ln(t)) is: (negative exponents allowed)

What is f'(t) =( (t^-5+ln(t))(-5e^-5t)-e^-5t(-5t^-4+1/x) )/((t^-5+ln(t))²)

Random!

100

d/dx[x³]

3x²

200

d/dx(xsinx)

xcosx+sinx

300

The derivative of f(x) = ln(e^x) is: 

1

400

d/dθ (θcscθ−cotθ)  

cscθ(−θcotθ+1+cscθ)

500

dy/dx if y=e^(7-9x)

−9e^(7−9x)