Solution 1.2:2b
From Förberedande kurs i matematik 2
The whole expression consists of two parts: the outer part, " \displaystyle e raised to something",
\displaystyle e^{\left\{ \left. {} \right\} \right.}
where "something" is the inner part
\displaystyle \left\{ \left. {} \right\} \right.=x^{2}+x. The derivative is calculated according to the chain rule by differentiating
\displaystyle e^{\left\{ \left. {} \right\} \right.}
with respect to
\displaystyle \left\{ \left. {} \right\} \right.
and then multiplying by the inner derivative
\displaystyle \left( \left\{ \left. {} \right\} \right. \right)^{\prime }, i.e.
\displaystyle \frac{d}{dx}e^{\left\{ \left. x^{2}+x \right\} \right.}=e^{\left\{ \left. x^{2}+x \right\} \right.}\centerdot \left( \left\{ \left. x^{2}+x \right\} \right. \right)^{\prime }
The inner part is an ordinary polynomial which we differentiate directly:
\displaystyle \frac{d}{dx}e^{\left\{ \left. x^{2}+x \right\} \right.}=e^{\left\{ \left. x^{2}+x \right\} \right.}\centerdot \left( 2x+1 \right)
