Calculus Derivatives

Basic Derivatives, Level 1

100

y = 3

y' = 0

200

f(x) = 5x²-2x+1,000,000

f'(x) = 10x - 2

300

f(x) = -3x - cot(x)

f'(x) = -3 + csc²(x)

400

f(x) = 3sinx - 2cosx

3cosx + 2sinx

500

y = 2tan(x) - 5sec(x)

y' = 2sec²(x) - 5sec(x)tan(x)

Basic Derivatives, Level 2

100

y = csc(x) + sec(x)

y' = -csc(x)cot(x) + sec(x)tan(x)

200

f(x) = (2-x³) / x²

f'(x) = -1 - 4/x³

300

y = 5lnx

y' = 5/x

400

f(x)=7^x

f'(x) = 7^x * ln7

500

y = ln (e^x)

y' = 1 

y=x because the functions are inverses

Product and Quotient Rule

100

y = 3x² sin x

y' = 3x² cos x + 6x sin x

200

y = (5x - 2)/(x² + 1)

simplify the numerator

y' = (-5x² + 4x + 5)/(x² + 1)²

300

f(x) = -2/(3x - 2x²)

f'(x) = (6 - 8x)/(3x - 2x²)²

400

f(x) = (2-x³) / x²

f'(x) = -1 - 4/x³

500

y = x³sin(x)

y' = x³cos(x) + 3x²sin(x)

Tangent and Normal Lines

100

Eq of Tangent Line

f(x) = 5x³

at x = -1

(y+5) = 15(x+1)

200

Eq of Tangent Line

f(x) = sinx

at x = pi/2

y = 1

300

Eq of Tangent Line

f(x) = 3/x

at x = 2

(y - 3/2) = -3/4 (x - 2)

400

Eq of Normal Line

f(x) = 3x² + 7x

at x = 1

(y - 10) = -1/13 (x - 1)

500

Eq of Normal Line

f(x) = cosx

at x = 3pi/2

y = -x + 3pi/2