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Derivative of Natural Logarithm ln(x² - 3x)

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Derivative – Natural Log Function

Calculate the derivative of a function ln(x² - 3x) with respect to the variable x using analytical differentiation.

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Jan 23, 2013
Derivative
by: Staff


Answer

Part I




f(x) = ln(x² - 3x)

d
---- ln(x² - 3x)
dx

note that:

d 1 du
---- ln(u) = --- * ----
dx u dx

therefore,

d 1 d
---- ln(x² - 3x) = ----------- * ---- (x² - 3x)
dx (x² - 3x) dx


d 1
---- ln(x² - 3x) = ----------- * (2x - 3)
dx (x² - 3x)

d (2x - 3)
---- ln(x² - 3x) = -----------
dx (x² - 3x)

Final Answer:


d (2x - 3)
---- ln(x² - 3x) = -----------
dx (x² - 3x)




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Jan 23, 2013
Derivative
by: Staff

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Part II

Graph of original function



Math – natural log function ln(x² - 3x)




Graph of derivative



Math – derivative of natural logarithm ln(x² - 3x)








Thanks for writing.

Staff
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