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Math 151-copyright Joe Kahlig, 19C Page 1 Section 3.6: Derivatives of Logarithmic Functions Derivative Formulas: y = ln(x) y = loga(x) Example: Find the derivative of these functions. 2 A) y = ln(5x −1) 2 x −5x B) y = ln(e +e ) 7 C) y = log4(x +3x) 2 D) y = elog(x +1) Math 151-copyright Joe Kahlig, 19C Page 2 2 E) y = 5xlog(cot(x )) 3 4 2 F) y = log5 (x+4) (x +1) 5 x +7 G) y = ln √ 5 4 x +2 Math 151-copyright Joe Kahlig, 19C Page 3 Logarithmic Differentiation Example: Find the derivative. cos(x) A) y = x 2x 3 e B) y = (x +7) Math 151-copyright Joe Kahlig, 19C Page 4 Example: Find the derivative. 3 4 5 8 y = (x +1) (x +2) 5 5 (6x +7)
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