Now let H––(t)=t3i–+t2j–+tk––𝐻_(𝑡)=𝑡3𝑖_+𝑡2𝑗_+𝑡𝑘_ be another vector function defined for each t∈R𝑡∈𝑅. The derivative of (F––(t)×G––(t)).H––(t)(𝐹_(𝑡)×𝐺_(𝑡)).𝐻_(𝑡) with respect to t𝑡, at t=1𝑡=1 is given by Answer

Let F––(t)=t2i–+tj–+k––𝐹_(𝑡)=𝑡2𝑖_+𝑡𝑗_+𝑘_ and G––(t)=i–+tj–+t2k––𝐺_(𝑡)=𝑖_+𝑡𝑗_+𝑡2𝑘_ be two vector functions defined for each t∈R𝑡∈𝑅. (a) The derivative of F––(t)×G––(t)𝐹_(𝑡)×𝐺_(𝑡) with respect to t𝑡, at t=1𝑡=1 is given by

Let F––(t)=t2i–+tj–+k––𝐹_(𝑡)=𝑡2𝑖_+𝑡𝑗_+𝑘_ and G––(t)=i–+tj–+t2k––𝐺_(𝑡)=𝑖_+𝑡𝑗_+𝑡2𝑘_ be two vector functions defined for each t∈R𝑡∈𝑅.

7. Find the gradient for the function 𝑢 = 𝜑(𝑟), 𝑟 = √𝑥2 + 𝑦2 + 𝑧2.Answer: 𝛁𝑢 = 𝜑′(𝑟) 𝒓𝑟 .

Differentiate the following functions w.r.t. 𝒙.(i) 8𝑥−34

The domain of the vector function F––(t)=t−3−−−−√i–+ln(10−2t−−−−−−√)–j+1t−3√k––𝐹_(𝑡)=𝑡−3𝑖_+𝑙𝑛(10−2𝑡)_𝑗+1𝑡−3𝑘_ is given by the interval