Let $z = \ln \left( x ^ { 2 } + 2 x y + 2 y \right) , x = t ^ { 2 } + 3 , y = t + \sqrt { t }$

question 76

Essay

Let $z = \ln \left( x ^ { 2 } + 2 x y + 2 y \right) , x = t ^ { 2 } + 3 , y = t + \sqrt { t }$ Find dz/dt at t = 1 using the chain rule.Give your answer to 4 decimal places.

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Definitions:

Mean

The mean of a collection of numbers, determined by dividing the total sum of the values by the count of the values.

Population

The entire collection of individuals or items considered for a study, from which samples are drawn for statistical analysis.

Population Mean

The average of a set of values or measurements taken from the entire population of interest.

Sample

A subset of a population selected for measurement, observation, or questioning, to provide statistical information about the whole.