Let r(t) = (t2, 1 – t, 4t). Calculate the derivative of r(t) · a(t) at t = 9, assuming that a(9) = (-7, –2, 2) and a' (9) = (-2, –9, 9) d r(t) · a(t)-9 dt

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

A:

Q: Differentiate the function. = In({ (4t+ 1)³ (4t-1)5 F'(t) = F(t) = In

A: The derivative of the function in the division form is given by the quotient rule which is given by-…

Q: Differentiate the function f(t) = t (11t+ 2). Answer f'(t) =

A:

Q: f(x, y) = e²+y² = e&+y?

A:

Q: Calculate the derivative of t2 -k 3 - t F(t) = cos(t) i + 3e2t+2j + |

A:

Q: f(t) = 1-2t 1 + 2t

A:

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

A: Given query is to find indicated derivative.

Q: 2. Determine the derivative of g(t) = 8°[(2t + 1)² + t].

A: Given that     g(t) = 8t[(2t+1)2+t]

Q: Find the derivative of the inverse of f for t = 0,

A: The derivative of a definite integral is given by the second fundamental theorem of calculus as…

Q: 49y" — 42y + 5y = 0, and - y(4) = 4, y'(4) = 1. y =

A: 49y''-42y'+5y=0, y(4)=4, y'(4)=1 Auxiliary equation 49m2-42m+5=0

Q: 50 Find the derivative of ƒ (t) = (3t³ – 6t2 + 11 )".

A: Explanation: Given that: ft=3t3-6t2+1150 Concept used: dxndx=nxn-1

Q: g(t) = V(1 – 3t)4 + t4

A:

Q: Differentiate the functions: 1. y = 3x – Vx 2. y = 2 – 3x – 3. Given the function f(x) = x³ – 5x +…

A: