Mathematics

Mathematics

Problem

Let h(x)=sin⁡2 ⁣((3x5+1)4)h(x)=\sin^{2}\!\bigl((3x^{5}+1)^{4}\bigr). Which of the following equals h′(x)h'(x)? a) 60x4(3x5+1)3sin⁡ ⁣((3x5+1)4)cos⁡ ⁣((3x5+1)4)60x^{4}(3x^{5}+1)^{3}\sin\!\bigl((3x^{5}+1)^{4}\bigr)\cos\!\bigl((3x^{5}+1)^{4}\bigr) b) 120(3x5+1)3sin⁡ ⁣((3x5+1)4)cos⁡ ⁣((3x5+1)4)120(3x^{5}+1)^{3}\sin\!\bigl((3x^{5}+1)^{4}\bigr)\cos\!\bigl((3x^{5}+1)^{4}\bigr) c) 120x4(3x5+1)3sin⁡ ⁣((3x5+1)4)cos⁡ ⁣((3x5+1)4)120x^{4}(3x^{5}+1)^{3}\sin\!\bigl((3x^{5}+1)^{4}\bigr)\cos\!\bigl((3x^{5}+1)^{4}\bigr) d) 120x4(3x5+1)4sin⁡ ⁣((3x5+1)4)cos⁡ ⁣((3x5+1)4)120x^{4}(3x^{5}+1)^{4}\sin\!\bigl((3x^{5}+1)^{4}\bigr)\cos\!\bigl((3x^{5}+1)^{4}\bigr)

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