EXAMPLE 1 Finding Partial Derivatives at a Point Find the values of of/ox and af/ay at the point (4, -5) if f(x, y) = x2 + 3xy + y 1. %3D
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- Q3 Find the minimum sum-of-products expressions for each of the following functions (d denotes don't care terms). (a) f(A, B, C, D) = Σm(4,11,12,13,14) + Σm(5,6,7,8,9,10) (b) f(A, B, C, D) = Σm(3,11,12,13,14) + Σm(5,6,7,8,9,10) (c) f(A, B, C, D) = m(1,2,4,13,14) + Σm(5,6,7,8,9,10) (d) f(A, B, C, D) = Σm(4,15) + Σd (5,6,7,8,9,10)Simplify the following Boolean functions, using Karnaugh maps: a. ?(?, ?, ?,?) = ∑(1,5,9,12,13,15)Consider the following functions: f₁(a, b, c) = Σm(0, 1, 3, 5) + d(2, 4) f₂(a, b, c) = Σm(1, 6) + d(2, 3, 5) How many functions are possible for f₁ + f₂?
- Simplify the following Boolean functions, using three-variable K-maps: F(A,B,C)= ∑(3,4,5,6,7)Find the simplest POS expression using K- Maps for the following functions. For each, list all prime implicants found in the K-Map, then list only the essential prime implicants, and then list the simplest solution. i. f (x1, x2, x3) = II M (0, 1, 2, 4, 5) ii. f (x1,x2, x3, x4) = ПМ (0, 1, 2,4, 5) Em (1, 2,5, 6, 7,8, 10, 14)Simplify the following two Boolean functions using K-MAP:c) F(A, B, X, D) = ∑ (2, 3, 10, 11, 12, 13, 14, 15) d) F(A, B, C, D) = ∑ (0, 2, 4, 5, 6, 7, 8, 10, 13, 15)
- Simplify the following Boolean functions, using three-variable K-maps: F(x, y, z)=Σ(1, 2, 3, 7)Q2: Find the derivative of: (1) y = sin(x* + V5) (2) y = 3x -5x +10 1+ sin x - sin x (3) y= tan %3DFind all the prime implicants for the following Boolean functions, and determine which are essential: F (A, B, C, D)=Σ(0, 2, 3, 5, 7, 8, 10, 11, 14, 15)