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 - x2 + 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 + x3-n + 13; n belongs
Answer: 2xn-1 + (3 - n)x2-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: y'' = 0.

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

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

Problem 22 y = x/(x + 5); x ≠ -5
Answer: $y'' = \frac{-10}{(x + 5)^3}$

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

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

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


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