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Find the Derivative of the Function y(x)=sec⁡(e4x)y ( x ) = \sec \left( e ^ { 4 x } \right)

Question 57

Multiple Choice

Find the derivative of the function. y(x) =sec⁡(e4x) y ( x ) = \sec \left( e ^ { 4 x } \right)


A) y′(x) =4e4xcsc⁡(e4x) tan⁡2(e4x) y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc \left( e ^ { 4 x } \right) \tan ^ { 2 } \left( e ^ { 4 x } \right)
B) y′(x) =16e4xsec⁡(e4x) tan⁡(e4x) y ^ { \prime } ( x ) = 16 e ^ { 4 x } \sec \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)
C) y′(x) =4e4xsec⁡(e4x) tan⁡(e4x) y ^ { \prime } ( x ) = 4 e ^ { 4 x } \sec \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)
D) y′(x) =4e4xcsc⁡2(e4x) tan⁡2(e4x) y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc ^ { 2 } \left( e ^ { 4 x } \right) \tan ^ { 2 } \left( e ^ { 4 x } \right)
E) y′(x) =4e4xcsc⁡(e4x) tan⁡(e4x) y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)

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