Define . Which of the following is equal to…

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

Problem

Define

S(x)=\displaystyle\int_{x}^{\arctan x} \sqrt{1+t^{4}}\,dt

. Which of the following is equal to

S'(x)

? (a)

\dfrac{\sqrt{1+(\arctan x)^{4}}}{1+x^{2}}+\sqrt{1+x^{4}}

(b)

\dfrac{\sqrt{1+(\arctan x)^{4}}}{1+x^{2}}-\dfrac{\sqrt{1+x^{4}}}{1+x^{2}}

(c)

\dfrac{\sqrt{1+(\arctan x)^{4}}}{1+x^{2}}-\sqrt{1+x^{4}}

(d)

\dfrac{x\sqrt{1+(\arctan x)^{4}}}{1+x^{2}}-\sqrt{1+x^{4}}