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 h(x)=[sec⁡(5x+1 )]3h(x)=\bigl[\sec\bigl(\sqrt{5x+1}\,\bigr)\bigr]^3. Which of the following is equal to h′(x)h'(x)? (a) 1525x+1 sec⁡2 ⁣(5x+1)tan⁡ ⁣(5x+1)\dfrac{15}{2\sqrt{5x+1}}\,\sec^{2}\!\bigl(\sqrt{5x+1}\bigr)\tan\!\bigl(\sqrt{5x+1}\bigr) (b) 152 sec⁡3 ⁣(5x+1)tan⁡ ⁣(5x+1)\dfrac{15}{2}\,\sec^{3}\!\bigl(\sqrt{5x+1}\bigr)\tan\!\bigl(\sqrt{5x+1}\bigr) (c) 1525x+1 sec⁡3 ⁣(5x+1)tan⁡ ⁣(5x+1)\dfrac{15}{2\sqrt{5x+1}}\,\sec^{3}\!\bigl(\sqrt{5x+1}\bigr)\tan\!\bigl(\sqrt{5x+1}\bigr) (d) 525x+1 sec⁡3 ⁣(5x+1)tan⁡ ⁣(5x+1)\dfrac{5}{2\sqrt{5x+1}}\,\sec^{3}\!\bigl(\sqrt{5x+1}\bigr)\tan\!\bigl(\sqrt{5x+1}\bigr)

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