Given f(x,y,z)=x2−2y2+z2,x(t)=sint,y(t)=et and z(t)=3t for 0≤t≤π (i) Find the directional derivative of f(x,y,z) at x=1

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Given f(x,y,z)=x2−2y2+z2,x(t)=sint,y(t)=et and z(t)=3t for 0≤t≤π (i) Find the directional derivative of f(x,y,z) at x=1 in the direction of the vector b=2i+j−2k. Give your answer in terms of π. [9 marks] (ii) Find dtdf​ in terms of t. [4 marks] (iii) Determine the exact value of dtdf​ when x=1. [2 marks]