a) If F(x) = | 1 dt, then F'(x) = t 14 1 b) If F(2) = dt, hen F'(2) = 1 c) If F(x) = / dt, then F'(x) t ニ rx²+1 1 c) If F(x) dt, then F' (x) = t 2+cos x

Q: Find f '(3), where f(t)= u(t)v(t), u(3) = (1, 2, -2), u'(3) = (7, 1, 5), and v(t) - (t, 2², 2³).…

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Q: 2x² Find F'(x) given that F(x) = S," cos (t2 + 2)dt

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Q: It takes a total of 12 hours to drain a tank by opening a valve at the bottom. The depth h (in…

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Q: clnx 5) cos et dt = d ftm a) COS X x b) cos(ln(x)) c) cos ex d) cos 1

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Q: Find f '(2), where f (t) = ü(t) · i(t), ü(2) = (1,2,–1), ū'(2) = (3,0,4), and v(t) = (t, t?,t3).

A: To find out the f'(2)

Q: 7) Find f(e) if a) f'(;) = { x and f6)=2 D f'(x)=\+sinx & f 3.

A: Here we find the f(x) using integration.

Q: Assume that a function F is defined by F(r) = dt. Then, F'(2) is given by (A) F'(2) = 4V3 4. (B)…

A: Topic:- application of derivatives and integration

Q: Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, -1), u'(3) = (5, 1, 4), and v(t) = (t, t², t³).…

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Q: Suppose F(x) = f(x² + 1). Find F'(1) if f'(2) = 9.

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Q: d dx

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Q: 4 Suppose that f'(x) = 2x for all x a) Find f(5) if f(0) = 0. b) Find f(5) if f(4) = 14. c) Find…

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Q: If fx) = x'(x – 2) then f"(1) equals" A -1e C 2 D -2 E

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Q: 1) If f(x) = x²(2), find f'(2)

A: f(x)=x2∫2xdtt2+5we know  d dx(∫axf(t)dt)=f(x)×d dx(x)-f(a)×d dx(a)

Q: Find the derivative (dy/dx) of the following functions: h) у%3D Зx7 —7х3 + 21x2 - i) y = (x² +…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: Let f(t) = (t² + 4t+8) (2t² + 3). Find f'(t). f' (t) = Find f'(5). f'(5)=

A: The given function

Q: = (t² + 5t + 5) (5t² + 4), find ƒ'(t). If f(t) f’(t) = Find ƒʼ(3). ƒ'(3) =

A:

Q: If f (x) = 3x²-2 4x+1 then f'(-1) =

A: Given

Q: If F(x)= J. x) = [", "+!dt then F'(x) dt , then F'(x)= /3 sint

A: If Fx=∫π3xt2+1sintdt, then evaluate the value of F'x.

Q: Find F'(0) if F'(x)= (1+x) (2+ x)² (3 + x)³ (4 + x)+.

A: Solve the given problem.

Q: Suppose f(x) = [ 6t² /1+t° dt .

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Q: Solve F'(t) = t+ F(t – u) cos u du, F(0)-= 4. %3D

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Q: If f (x) = 2 x³ + 8 x² + 3, at what points are f '(x) zero or does not exist ? 8 0, 3 A 8 B 0, 3 1,…

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Q: If f(x) = t*dt then f'(x) =

A: Let, Substitute this in the given integral.

Q: Find f'(2), where f(t) = u(t) - v(t), u(2) = (1, 2, -1), u'(2) = (8, 1, 6), and v(t) = (t, t², t³).…

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Q: ゆ+

A: f(x)=axbx+1we know ddx(uv)=v*ddx(u)-u*ddx(v)v2ddx(f(x))=f'(x)

Q: Let F(x) · = 'X 1 13 (t+t7)20 dt. Then

A: