Class Notes - 11.1 - Der. of Logs PDF

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CLASS NOTES 11.1 DERIVATIVES OF LOGARITHMIC FUNCTIONS DEFINITION: Let u be a differentiable function of x. Then if y  log a u,

dy 1 1 du    dx ln a u dx

This is the most generalized form of the definition for the derivative of logarithms. Remember that ln x is the same as the log base e of x. EXAMPLE

Find the derivative of y  ln x

By definition dy  1  1  dx dx

ln e x dx

EXAMPLE

Find the derivative of y  ln 1  x2 

1 1 d (1  x 2 ) By definition dy    2 dx

ln e 1  x

dx

Use the properties of logarithms to simplify them before finding the derivative. EXAMPLE

Find

dy when dx

y  ln 1  x 

3/2

EXAMPLE Find the derivative of

y  ln  x 1x  2  



EXAMPLE





Find the derivative of y  log5 3x2  2

EXAMPLE

Find the relative max/min of y  x2 ln x

Assignment: Section 11.1 – 3, 7, 11, 13, 15, 20, 28, 29, 31, 43...