Calculus

Derivatives

100

Find the derivative of 9x³ + 4x - 7

27x²+4

200

Find the derivative of 8ln(x) + log₃x

8/x + 1/x * 1/ln3

300

Find the derivative of 47^x

47^xln47

400

Find the derivative of sqrt(x) + 3/x² (Give in fraction form!)

1/2sqrt(x) - 6/x³

500

Find the derivative of sqrt(x) + 12e^x - 7cos(x) (Give in fraction form!)

1/2sqrt(x) + 12e^x + 7sin(x)

Implicit Diff.

100

Find the differentiation of 2y = 7x + 1

dy/dx = 7/2

200

Find the differentiation of 5y² + 3 = x²

dy/dx = x/5y

300

Find the differentiation of 2y² + 10y = 6x

dy/dx = 3/(2y+5)

400

Find the differentiation of 3 + y⁴ = 8xy

dy/dx = 2y/(y³ - 2x)

500

Find the differentiation of sin(y²) + 17 = 6x

dy/dx = 3sec(y²)/y

Chain Rule

100

I got bored and decided to throw in a random question. This player has scored the second most points in a single game in NBA history with 81. Name this leader in points scored for the Los Angeles Lakers, with 33,643 points.

Who is Kobe Bryant?

200

y = ln(x⁹)

9/x

300

y = cos(5x)

-5sin(5x)

400

y = sin(ln(x⁵))

(5/x)cos(ln(x⁵))

500

y = 1/(4x²+7)³

-24/(4x²+7)⁴

Trig

100

Find the derivative of 12 - cot(x)

csc²x

200

Find the derivative of 1/(3sin(x))

-(1/3)csc(x)cot(x)

300

Find the derivative of tan^-1(5x)

5/(25x²+1)

400

Evaluate the function f(x) = arccos(x/6) at x = 3

π/3

500

Find the derivative of arcsec(x⁶)

6/(|x|sqrt(x¹²-1))

Product & Quotient

100

Find the derivative of 4x⁵e^x

4x⁵e^x + 20x⁴e^x

200

Find the derivative of sin(x)/x

(xcos(x) - sin(x))/x²

300

Find the derivative of 3x³sin(x)

3x³cos(x) + 9x²sin(x)

400

Find the derivative of (3/x)ln(x)

(3 - 3ln(x))/x²

500

Find the derivative of (2x + 4)/(3x + 2)

-8/(3x+2)²