Which of the following limits equals the derivative of at ?

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Which of the following limits equals the derivative of ln⁡x\ln x at x=5x=5? (a) lim⁡h→0ln⁡(5+h)−ln⁡55h\displaystyle \lim_{h\to 0} \dfrac{\ln(5+h)-\ln 5}{5h} (b) lim⁡h→0ln⁡(5+h)−ln⁡5h\displaystyle \lim_{h\to 0} \dfrac{\ln(5+h)-\ln 5}{h} (c) lim⁡h→0ln⁡(5h)−ln⁡5h\displaystyle \lim_{h\to 0} \dfrac{\ln(5h)-\ln 5}{h} (d) lim⁡h→0ln⁡(5+h)h\displaystyle \lim_{h\to 0} \dfrac{\ln(5+h)}{h}

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