Let . Which of the following is equal to…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let f(x)=sec⁡(3x2+1)f(x)=\sec\bigl(\sqrt{3x^{2}+1}\bigr). Which of the following is equal to f′(x)f'(x)? (a) 6x sec⁡(3x2+1)tan⁡(3x2+1)6x\,\sec\bigl(\sqrt{3x^{2}+1}\bigr)\tan\bigl(\sqrt{3x^{2}+1}\bigr) (b) 3x sec⁡(3x2+1)tan⁡(3x2+1)3x\,\sec\bigl(\sqrt{3x^{2}+1}\bigr)\tan\bigl(\sqrt{3x^{2}+1}\bigr) (c) 3x sec⁡(3x2+1)tan⁡(3x2+1)3x2+1\displaystyle \frac{3x\,\sec\bigl(\sqrt{3x^{2}+1}\bigr)\tan\bigl(\sqrt{3x^{2}+1}\bigr)}{\sqrt{3x^{2}+1}} (d) 3x sec⁡(3x2+1)cot⁡(3x2+1)3x2+1\displaystyle \frac{3x\,\sec\bigl(\sqrt{3x^{2}+1}\bigr)\cot\bigl(\sqrt{3x^{2}+1}\bigr)}{\sqrt{3x^{2}+1}}

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