Explain 2 sources of laboratory error when it comes to recrystallization.

One source of error is losing purified product on the filter. Another is not using a volatile enough solvent, which would cause more solvent to remain on the product after recrystallization.

Using your knowledge of evolution, describe how mutations and be random, while the trajectory of evolution is non-random.

Mutations are random due to errors in DNA replication. These errors are indeed random mistakes. However, the effect that these mutations have on the fitness of an organism are not. If a mutation increases the ability of an organism to survive or thrive, the mutation will remain within the population and guide evolutionary trajectory. On the other hand, if the mutation is detrimental to the organism's survival, the mutation will be weeded out of the population. This process of evolution is strictly non-random: if a mutation is beneficial, it will remain.

Using chain rule, evaluate the following derivative: d/dx (3 x^{2} - 2x)^5

(5(3 x^{2} - 2x)^4)*(6x-2)