Derivatives Extra Practice

Power Rule/Sum/Difference

100

f^' of f(x) = -4x⁵

-20x⁴

200

f^' of f(x) = x² + 4x + 2

2x + 4

300

f^' of f(x) = (2/3)x⁴ - 3x²

(8/3)x³ - 6x

400

f^' of f(x) = (4x² - 3x)/5

(8x - 3)/5

500

f^' of f(x) =ax^b + x(c - d)³

abx^b-1 + (c - d)³

Product/Quotient

100

f^' of f(x) = (3x²)/(x^5/2)

(-3)/(2x^3/2)

200

f^' of f(x) = x³(1 - 2x²)

x²(3 - 10x²)

300

f^' of f(x) = (3x²)/(1 - 2x)

[6x(1 - 3x)]/[(1 - 2x)²]

400

f^' of f(x) = (4x²)/(1 - x^7/3)

[4x(6 + x^7/3)]/[3(1 -  x^7/3)²]

500

f^' of f(x) = (1 + x)^3/2(x⁴)

[x³(1 + x)^1/2(11x + 8)]/2

Higher Order

100

f^'' of f(x) = 3x³

18x

200

f^'' of f(x) = 2x² - 4x + 6

4

300

a(t) of s(t) = -4.9t² + 13t + 27

-9.8

400

f^'' of f(x) = g(x)h(x)

g(x)h^''(x) + 2g^'(x)h^'(x) + h(x)g^''(x)

500

g^''' of g(x) =(1 - x)⁴

-24(1-x)

Chain Rule

100

f' of f(x)=sin(6x)

6cos(6x)

200

f' o f(x) = (x² - 1)³

6x(x² - 1)²

300

f' of f(x) = cos²(x² - 4)

-4x cos(x² - 4)sin(x² - 4)

400

f' of f(x) = (4 - x⁴)^-1/2

2x³(4 - x⁴)^-3/2

500

g" of g(x) = sin²(4x)

Preferred: 32cos 8x

Equivalent: 32(cos²4x - sin²4x)

Final Jeopardy

100

Whenever You Are Ready!

Prove the Quotient Rule by using the Chain Rule