A) \[{{x}^{x}}{{e}^{\left( 2x+5 \right)}}\,\left( 2+\log \,\,x \right)\]
B) \[{{x}^{x}}{{e}^{\left( 2x+5 \right)}}\,\left( 3+2\,\log \,x \right)\]
C) \[{{x}^{x}}\,{{e}^{\left( 2x+5 \right)}}\,\,\left( 2+3\,\log \,x \right)\]
D) \[{{x}^{x}}\,{{e}^{\left( 2x+5 \right)}}\,\left( 3+\log \,x \right)\]
Correct Answer: D
Solution :
\[y={{x}^{x}}.{{e}^{\left( 2x+5 \right)}}\] \[\Rightarrow \,\log y=x\,\log \,x+\left( 2x+5 \right)\] \[\Rightarrow \frac{1}{y}.\frac{dy}{dx}=\left( x.\frac{1}{x}+\log \,x \right)+2\] \[\Rightarrow \,\frac{dy}{dx}={{x}^{x}}.{{e}^{2x+5}}.\left( 3+\log \,x \right)\]
You need to login to perform this action.
You will be redirected in
3 sec
