Gamify mortega22

EXPONENTIAL DERIVATIVES

100

Differentiate this equation: e^5x

5e^5x

200

Differentiate this equation: a^x

ln(a) * a^x

300

Differentiate this equation: 2e^x - 8^x

2e^x - 8^x * ln(8)

400

Differentiate this equation: e^{-x^3}

−3x²e^{-x^3}

500

Differentiate this equation: 4^{3x^2}

6x4^{3x^2} * ln (4)

LOGARITHMIC DERIVATIVES

100

Differentiate this equation: ln(x)

1/x

200

Differentiate this equation: log₅(x)

1/(xln(5))

300

Differentiate this equation: log₃(x−4x²)

(1 - 8x)/((x - 4x²)ln3)

400

Differentiate this equation: ln(1+2x²−5x³)

(4x−15x²)/(1+2x²-5x³)

500

Differentiate this equation: ln(8+3x)

3/(8+3x)

TRIG DERIVATIVES

100

Differentiate this equation: 5 sin(x)

5 cos(x)

200

Differentiate this equation: 6 cos(7x)

-42 sin(7x)

300

Differentiate this equation: 8 sin(5(x - 9)) + 10

40 cos(5(x - 9))

400

Differentiate this equation: x⁴ * tan(x)

4x³tan(x) + x⁴sec(2x)

500

Differentiate this equation: sin²(x)cos³(x)

2sin(x)cos⁴(x) − 3sin³(x)cos²(x)

POWER/QUOTIENT RULE

100

Differentiate this equation: 6x⁴ * 8x

240x⁴

200

Differentiate this equation: 2 / (2x⁴ − 5)

16x³ / (4x⁸ − 20x⁴ + 25)

300

Differentiate this equation: (2x⁴ − 3)(x² + 1)

12x⁵ + 8x³ − 6x

400

Differentiate this equation: (5x⁴ − 3x² − 1)(−5x² + 3)

−150x⁵ + 120x³ − 8x

500

Differentiate this equation:  (x³ − x² − 3) / (x⁵ + 3)

(−2x⁷ + 3x⁷ + 15x⁴ + 9x² − 6x) / (x¹⁰ + 6x⁵ + 9)

MISC.

100

Differentiate this equation: 7 cos(8x)

-56 cos(8x)

200

Differentiate this equation: 2 / (x⁵ − 5)

10x⁴ / (x¹⁰ − 10x⁵ + 25)

300

Differentiate this equation: (x⁴ + 3)(−4x⁵ + 5x⁴ + 5)

−36x⁸ + 40x⁷ − 60x⁴ + 80x³

400

Differentiate this equation: 555^x

ln(555) * 555^x

500

Differentiate this equation: xe^x * cos(x)

e^xcos(x) + x(e^xcos(x) - e^xsin(x))