Higher-Order DifferentiationIn Exercises 23–26, find (a)
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- YouTrylt 1 Find the derivative of the vector function. r(t) =(t sint, , t cos(21 )) C. r(t) =( tant, sect, d.arrow_forwardConsider the R − R 2 function r defined by r (t) = t, t2 ; t ∈ [−3, 3] . (a) Determine the vector derivative r 0 (1) (b) Sketch the curve r together with the vector r 0 (1), in order to illustrate the geometric meaning of the vector derivative.arrow_forwardWhy is r(t) = ⟨ƒ(t), g(t), h(t)⟩ called a vector-valued function?arrow_forward
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- B- Find the directional derivative of the function W = x² + xy + z³ at the point P: (2,1,1) in the direction towards P₂(5,4,2). əz Ju əv B- If Z = 4e* Iny, x = In(u cosv) and y = u sinv find andarrow_forwardcalculate r(t) and T(t), and evaluate T(1). r(t) = (et, t2)arrow_forward(a) Find the direction for which the directional derivative of the function f(x, y, z)=√x² + y² + z² is a maximum at P = (8,5, 2). (Use symbolic notation and fractions where needed. Give your answer in vector form.)arrow_forward
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