Math10.com

Bulgarian

List of Derivative Problems

(1 - 18) Find the derivative of:

Problem 1 y = 3a; a = const.
Answer: 0.

Problem 2 y = 5x - 4
Answer: 5.

Problem 3 y = (√2x - 3)/6
Answer: √2/6.

Problem 4 y = 8 -2x/5
Answer: -2/5.

Problem 5 y = 0,5x²
Answer: x

Problem 6 y = 3x² + √7x + 1
Answer: 6x + √7.

Problem 7 y = 1 - x + x - 3x⁴
Answer: -2x + 1 - 12x³.

Problem 8 y = -x³ + 4x² - 5
Answer: -3x² + 8x.

Problem 9 y = 5x³ - √2x² + 6x
Answer: 15x² - 2√2x + 6.

Problem 10 y = 2xⁿ + x^3-n + 13; n
Answer: 2x^n-1 + (3 - n)x^2-n.

Problem 11 y = (x - 1)(x² + 3)
Answer: 3x² - 2x + 3.

Problem 12 y = x⁴/4 - x^-8
Answer: x³ + 8x^-9.

Problem 13 y = x/2 + 2/x
Answer: 1/2 - 2/x².

Problem 14 y = (x + 2)² - 5x³
Answer: -15x² + 2x + 4.

Problem 15 y = x(x² - 3)(x³ + 1)
Answer: 6x⁵ - 12x³ + 3x² - 3.

Problem 16 y = (ax + 1)² - 2ax³; a = const
Answer: 6ax² + 2a²x + 2a.

Problem 17 y = (2x² - 4x)√x; x > 0
Answer: (5x - 6)√x.

Problem 18 y = √x/(x + 3); x > 0
Answer: (3 - x)/2√x(x + 3)².

(19 - 25) Find the second derivative of:

Problem 19 y = 8x - 3
Answer: 0.

Problem 20 y = 12x² - 16x + 4
Answer: 24.

Problem 21 y = x³ - 4x² + 1/x; x ≠ 0
Answer: 6x - 8 + 2/x³.

Problem 22 y = x/(x + 5); x ≠ -5
Answer: -10/(x + 5)².

Problem 23 y = cos 3x
Answer: -9cos3x.

Problem 24 y = sin³x
Answer: 9sin³x - 6sinx.

Problem 25 y = √x + 4/4; x ≥ -4
Answer: 1/4.√(x + 4)³.