4'5 Derivatives of logarithms

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4.5 Derivatives of logarithms
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The function is the natural logarithmic
function. Ln means log base e. The function has
domain xgt 0 and the derivative of the natural log
function is given by
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Find each derivative
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Use the chain rule to differentiate a function
with form lng(x).
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Find each derivative
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The properties of logarithms may be used to
simplify the process of differentiation. These
are covered in Mth 112.
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Find each derivative
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Find the equation of the tangent line to the
graph of the function
at the point (1, 6).
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Suppose that the demand for a certain product is
given by
(a) Find the revenue function (b) Find the
marginal revenue function (c) Find the marginal
revenue when the production level is 50 units.
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The demand for a new computer game can be modeled
by p(x) 53.5 8ln x,where p(x) is the price
consumers will pay in dollars and x is the number
of games in thousands.(a) Find R(x)(b) Find the
marginal revenue(c) Is there a price at which
revenue will be maximized?