Using the product rule, quotient rule or chain rule, differentiate each ofthe following functions.i. f (x) = 6x19e−4xii. f (x) = ln(3 x9 + 4)

Question

Using the product rule, quotient rule or chain rule, differentiate each ofthe following functions.i. f (x) = 6x19e−4xii. f (x) = ln(3 x9 + 4)
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Solution 1

i. To differentiate the function f(x) = 6x^19 * e^(-4x), we will use the product rule which states that the derivative of a product of two functions is the derivative of the first times the second plus the first times the derivative of the second.

Let's denote u = 6x^19 and v = e^(-4x).

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