Differentiate.
-$\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { 3 \mathrm { x } } \tan \left( \mathrm { x } ^ { 2 } \right)$
A) 3 $e ^ { 3 x }$ tan $x ^ { 2 }$ + 2x $e ^ { 3 x }$ $\sec ^ { 2 }$ ( $x ^ { 2 }$ )
B) 6x $e ^ { x }$ $\sec ^ { 2 }$ $x ^ { 2 }$
C) 3 $e ^ { x }$ $\sec ^ { 2 }$ $x ^ { 2 }$
D) 3 $e ^ { x }$ tan $x ^ { 2 }$ + $e ^ { 3 x }$ $\sec ^ { 2 }$ $x ^ { 2 }$
E) none of these

Question

Differentiate. 
-$\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { 3 \mathrm { x } } \tan \left( \mathrm { x } ^ { 2 } \right)$
A) 3 $e ^ { 3 x }$ tan $x ^ { 2 }$ + 2x $e ^ { 3 x }$ $\sec ^ { 2 }$ ( $x ^ { 2 }$ )
B) 6x $e ^ { x }$ $\sec ^ { 2 }$ $x ^ { 2 }$
C) 3 $e ^ { x }$ $\sec ^ { 2 }$ $x ^ { 2 }$
D) 3 $e ^ { x }$ tan $x ^ { 2 }$ + $e ^ { 3 x }$ $\sec ^ { 2 }$ $x ^ { 2 }$
E) none of these

Quizplus · Accepted Answer

The differentiation of $f(x) = e^{3x} \tan(x^2)$ using the product rule and chain rule gives $f'(x) = 3e^{3x} \tan(x^2) + 2x e^{3x} \sec^2(x^2)$.

Differentiate f(x)=e3xtan⁡(x2)\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { 3 \mathrm { x } } \tan \left( \mathrm { x } ^ { 2 } \right)f(x)=e3xtan(x2)

Differentiate $\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { 3 \mathrm { x } } \tan \left( \mathrm { x } ^ { 2 } \right)$