Find the derivative of the function. $y ( x ) = \sec \left( e ^ { 4 x } \right)$
A) $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc \left( e ^ { 4 x } \right) \tan ^ { 2 } \left( e ^ { 4 x } \right)$
B) $y ^ { \prime } ( x ) = 16 e ^ { 4 x } \sec \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)$
C) $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \sec \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)$
D) $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc ^ { 2 } \left( e ^ { 4 x } \right) \tan ^ { 2 } \left( e ^ { 4 x } \right)$
E) $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)$

Question

Find the derivative of the function.   $y ( x ) = \sec \left( e ^ { 4 x } \right)$ 
A) $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc \left( e ^ { 4 x } \right) \tan ^ { 2 } \left( e ^ { 4 x } \right)$
B) $y ^ { \prime } ( x ) = 16 e ^ { 4 x } \sec \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)$
C) $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \sec \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)$
D) $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc ^ { 2 } \left( e ^ { 4 x } \right) \tan ^ { 2 } \left( e ^ { 4 x } \right)$
E) $y ^ { \prime } ( x ) = 4 e ^ { 4 x } \csc \left( e ^ { 4 x } \right) \tan \left( e ^ { 4 x } \right)$

Quizplus · Accepted Answer

The derivative of $y(x) = \sec(u)$, where $u = e^{4x}$, is given by $y'(x) = \sec(u) \tan(u) \cdot u'$, where $u' = \frac{d}{dx}e^{4x} = 4e^{4x}$. Therefore, $y'(x) = 4e^{4x} \sec(e^{4x}) \tan(e^{4x})$.

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

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