(A) Differentiate $e ^ { 2 x }$ By Differentiating $e ^ { x } \cdot e ^ { x }$

Essay

(a) Differentiate $e ^ { 2 x }$ by differentiating $e ^ { x } \cdot e ^ { x }$ .(b) Differentiate $e ^ { 3 x }$ by differentiating $e ^ { x } e ^ { 2 x }$ and using the result of part (a).(c) Continue as above to find $\frac { d } { d x } e ^ { 4 x } \text { and } \frac { d } { d x } e ^ { 5 x }$ using the results from above.(d) Based upon your answers to parts (a)-(c), make a conjecture about $\frac { d } { d x } e ^ { n x }$ .