Class 11 Maths | Properties of Differentiation (Part 1) – Basics of Advanced Maths
Class 11 Maths | Properties of Differentiation (Part 1) – Basics of Advanced Maths

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Use the properties of the derivative to find the following:
r(t) = ti + Stj + tk,
u(t) = Sti + t^2j + tk
(a) r'(t) = (1, 5, 2t)
-[2r(t) u(t)]
3, 10 – 2t, 4t 322
-[(3t)u(t)]
301, 922, 1283
-[r(t) u(t)]
[r(t) u(t)]
r(4t)

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01:37

Use the properties of the derivative to find the following: r(t) = ti + Stj + +k, u(t) = 4ti + tj + tk(a) r(t)(b) -[Zr(t) u(t)](c) d[(2t)u(t)](d) [r(t) u(t)](e) dt [r(t) u(t)]r(2t)

01:16

Use the properties of the derivative to find the following. r(t) = ti + 4tj + t^2k, u(t) = 5ti + t^2j + t^3kf) d/dt r(3t)

01:23

Use the properties of the derivative to find the following.

r(t) = 9ti + (t âˆ’ 1)j, u(t) = ti + t^2j + (4/3)t^3k

(a) r'(t)(b) d/dt [u(t) âˆ’ 2r(t)](c) d/dt [(2t)r(t)](d) d/dt [r(t) Â· u(t)](e) d/dt [r(t) âœ• u(t)](f) d/dt [u(2t)]

05:29

Use the properties of the derivative to find the following:

r(t) = 3ti + (t – 1)j, u(t) = ti + t^2j + 2t^3k

(a) r(t)3i + j

(b)[u(t) – 2r(t)]5i + (2t – 2)j + 2/k

(c)[(2t)r(t)]12ti + (4t – 2)j

(d)[r(t) u(t)]32t^2 + 7t

(e)[r(t) x u(t)][u(2t)]

07:42

Use the properties of the derivative to find the following: r(t) = ti + 4tj + tZk, u(t) = 4ti + t^2j + 3k

(a) r(t) + u(t) = i + 4j + 2tk (b) 2r(t) – u(t) = 2i + 8j – 2tj (c) 4t – 3u(t) = 12t – 3t^2j (d) -[(3t)u(t)] = -3t^3j (e) [r(t) u(t)] = 4t^2j (f) [r(t) u(t)] = 4t^2j (g) r(3t) = 3ti + 12tj + 3tk

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