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In this lesson, we will learn how to determine the derivatives of vector-valued functions in one variable by taking the derivative of each component.

Q1:

Calculate π β² ( π ) , and find the vector form of the equation of the tangent line πΏ at π ( 0 ) for π ( π ) = ( 2 π , 2 π , π ) c o s s i n .

Q2:

Calculate π β² ( π ) , and find the vector form of the equation of the tangent line at π ( 0 ) for π ( π ) = οΉ π + 1 , π + 1 , π + 1 ο 2 3 .

Q3:

Calculate f β² ( π ) , and find the vector form of the equation of the tangent line at f ( 0 ) for f ( π ) = ( π + 1 , π + 1 , π + 1 ) π 2 π π 2 .

Q4:

Consider the curve . Determine and find the tangent to the curve when .

Q5:

Given that , where and are constants, find .

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