Differentiate.
-$e ^ { x ^ { 2 } }$ + 2 ln( $x ^ { e }$ )
A) 2 $e ^ { x }$ + 2 $\frac { 1 } { \ln \left( x ^ { \mathrm { e } } \right) }$ ∙ $x ^ { e }$
B) 2x $e ^ { x ^ { 2 } }$ + 2e $\frac { 1 } { x }$
C) $x ^ { 2 }$ $e ^ { x ^ { 2 } - 1 }$ + 2e $\frac { 1 } { \mathrm { x } ^ { \mathrm { e } } }$ ∙ $x ^ { e }$ - 1
D) none of these

Question

Differentiate. 
-$e ^ { x ^ { 2 } }$ + 2 ln( $x ^ { e }$ )
A) 2 $e ^ { x }$ + 2 $\frac { 1 } { \ln \left( x ^ { \mathrm { e } } \right) }$ ∙ $x ^ { e }$
B) 2x $e ^ { x ^ { 2 } }$ + 2e $\frac { 1 } { x }$
C) $x ^ { 2 }$ $e ^ { x ^ { 2 } - 1 }$ + 2e $\frac { 1 } { \mathrm { x } ^ { \mathrm { e } } }$ ∙ $x ^ { e }$ - 1
D) none of these

Quizplus · Accepted Answer

The differentiation of $e^{x^2}$ using the chain rule is $2x e^{x^2}$, and the differentiation of $2 \ln(x^e)$ is $2e \frac{1}{x}$ by applying the chain rule and the derivative of the natural logarithm.

Differentiate ex2e ^ { x ^ { 2 } }ex2 + 2 Ln

Differentiate $e ^ { x ^ { 2 } }$ + 2 Ln