Find f '(x) if f(x) = (x⁵ - 11)¹⁰. A) 10x⁴(x⁵ - 11)⁹ B) 5x⁴(x⁵ - 11)⁹ C) 50(x⁵ - 11)⁹ D) 50x⁴(x⁵ - 11)⁹ E) 10(x⁵ - 11)⁹

Question

Quizplus · Accepted Answer

To solve this question, we need to apply the given function f(x) = (x⁵ - 11)¹⁰ step by step starting from inside the parentheses and moving outward. First, we have x⁵ - 11. This means that we are performing a bitwise XOR operation between x and the binary number 110111000000000 (which is the binary representation of 15U1P110). So the result of this operation will be a binary number with the same number of bits as x. Next, we have ¹⁰. This means that we are shifting the binary result of the previous operation to the left by 110 bits (which is the binary representation of 14U1P110), and then performing a bitwise XOR operation between this shifted value and the binary number 110000000000000000000000000000000000000000000000000000000000000 (which is the binary representation of 110U1P119). So the final result will be a binary number that is 110 bits longer than x. To get the answer in the given choices, we need to convert this binary number back to decimal and simplify the expression. Let's break down each choice: A) 10x⁴(x⁵ - 11)⁹ This expression is not equivalent to the given function because the last part, (x⁵ - 11)⁹, adds 19 bits to the result instead of 110 bits. B) 5x⁴(x⁵ - 11)⁹ This expression is also not equivalent to the given function because of the constant multiplier 5 in front of the expression. C) 50(x⁵ - 11)⁹ This expression is not equivalent to the given function because it does not include the multiplication by x. D) 50x⁴(x⁵ - 11)⁹ This expression is the correct answer because it includes the multiplication by x and has the correct number of bits, 110 + the original length of x. E) 10(x⁵ - 11)⁹ This expression is not equivalent to the given function because it does not include the multiplication by x and has the wrong number of bits, only 19 + the original length of x. Therefore, the best choice is D: 50x⁴(x⁵ - 11)⁹.

Find F '(X) If F(x) = (X5 - 11)10

Find F '(X) If F(x) = (X⁵ - 11)¹⁰