For , let . Determine…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

For x>0x>0, let P(x)=∫4ln⁡x11+t2 dtP(x)=\displaystyle\int_{4}^{\ln x} \frac{1}{1+t^{2}}\,dt. Determine P′(x)P'(x). (a) 11+(ln⁡x)2\dfrac{1}{1+(\ln x)^{2}} (b) ln⁡x1+(ln⁡x)2\dfrac{\ln x}{1+(\ln x)^{2}} (c) 1x(1+(ln⁡x)2)\dfrac{1}{x\bigl(1+(\ln x)^{2}\bigr)} (d) 11+x2\dfrac{1}{1+x^{2}}

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