MA 113 Exam 2 Review

Derivative Fun

100

x² + 2x - 4

2x + 2

200

sqrt(x⁴ + 2)

(2x³) / (sqrt(x⁴ + 2))

300

(x⁴ - 3x)(x + 4)²

(4x³ - 3)(x + 4)² + 2(x⁴ - 3x)(x + 4)

400

(x² + 2) / (3x)

(2x(3x) - 3(x² + 3)) / (3x)²

Get Triggy with It

100

cos(4x)

-4sin(4x)

200

sin(cos(x²))

-cos(cos(x²))(sin(x²))(2x)

300

tan^-1(3x² + 2)

(6x) / (1 + (3x² + 2)²)

400

cos²(sec(sqrt(x)))

2cos(sec(sqrt(x)))(-sin(sec(sqrt(x))))(sec(sqrt(x))tan(sqrt(x)))(1 / (2sqrt(x)))

e and ln

100

e^2x

2e^2x

200

ln(7x² + pi)

(14x) / (7x² + pi)

300

2e^{ln(e^(x^2))}

4x

400

ln((6x) / (3x²))

-1 / x

Implicit Differentiation

100

y = xy

y' = y / (1 - x)

200

2x = 3y - sin(y)

y' = 2 / (3 - cos(y))

300

ln(y²) + e^y = x³

y' = (3x²) / ((2 / y) + e^y)

400

e^xy = 2x - 3y²

y' = (2 - ye^xy) / (6y + xe^xy)

Drop it Like it's HOD

100

x² + 2x - 4

2

200

3sqrt(x) + 4x - 2

-3 / (4sqrt(x³))

300

sin(x³)

-sin(x³)(9x⁴) + cos(x³)(6x)

400

xe^x

2e^x + xe^x