. Let r(t) = (t², 1 t, 4t). Calculate the derivative of r(t) · a(t) at t = 6, assuming that a(6) = (9, −2, −2) and aʼ(6) = (2, 7, −8) d dt _r(t) · a(t)|t=6 · · = [ -0

Q: Evaluate the derivative of the function r(t)=⟨lnt,3t+1,t2⟩ at t=1.

A:

Q: Find the second, third, and fourth order derivatives of: y= f(x )= ax7 + bx3 + c y= f(x) = 3x/1-x…

A: It is simple derivative

Q: You have not submitted your answer. Find the derivative of the following function F(a)(2t 1) dt…

A: Use fundamental theorem of calculus and compute the derivative of the function

Q: By using the definition of the derivative, use a clear diagram to argue that d S(t)dt = f(x). %3D dx…

A: We have to prove that ddx∫axftdt=fx This will be prove by Newton's Leibnitz rule in this rule we…

Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

A:

Q: Find the derivative of y with respect to x. y = cos1 (5x2 + 4) 10x + (5x2 + 4)2 -10x Vi- (5x2 + 4)?…

A: The given function is  y= cos-1(5x2+4)  We have to find the derivative of this function w.r.t. x

Q: Find the derivative of f (t) = (6t3³ - 8t² + 7) 46 f' (t) = BA

A: Given query is to find indicated derivative.

Q: The sign x (t) is even symmetric and the sign y (t) is equal to the derivative of x (t). Show that…

A: even symmetric means it satisfies x(t)= x(-t) while odd symmetric means it satisfies x(-t)= -x(t)

Q: g(t) = V(1 – 3t)4 + t4

A:

Q: I. Find the derivative of the following functions: a. f(r) = 23 + 6x b. h(r) = (3r + 4)2 c. y = Vr3

A: According to company rules, I need to solve first 3 subparts when multiple subparts are posted