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Multiple Choice
Find the derivative of the given function. f(x)=8log2x
A
2lnx8
B
xln28
C
x8
D
xln81
Verified step by step guidance
1
Identify the function for which you need to find the derivative: f(x) = 8 * log_2(x).
Recall the change of base formula for logarithms: log_b(x) = log_c(x) / log_c(b). Here, we can use the natural logarithm (ln) as the base: log_2(x) = ln(x) / ln(2).
Substitute the change of base formula into the function: f(x) = 8 * (ln(x) / ln(2)).
Differentiate the function using the constant multiple rule and the derivative of ln(x): f'(x) = 8 * (1 / (x * ln(2))).
Simplify the expression to find the derivative: f'(x) = 8 / (x * ln(2)).