Question 8 - A-Level Maths

State the derivative of $\mathrm { e } ^ { \cos x }$.
Hence use integration by parts to find the exact value of $$\int _ { 0 } ^ { \frac { 1 } { 2 } \pi } \cos x \sin x \mathrm { e } ^ { \cos x } \mathrm {~d} x$$