Let f (t) = e5t sin 4t Part (a) Find L{f (t)} Part (b) Find L{f' (t)}

Q: Find f.  f''(t)=sin t + cos t,    f(0)=2,    f'(0)=4f f(t)= ?

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Q: Let f(x) = 2ln(sin(x)) ƒ''(x) =

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Q: ft= VTt tan t

A: Given:     ft=1+tan t9 Taking derivative on both sides    f't=ddt1+tan t19 Apply power rule:…

Q: If f(t) = (2t - ), find ƒ' (t).

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Q: If f(x) = 6 sin¯¹(x²), find ƒ'(x). Find ƒ'(0.5).

A: This question is related to differentiation, We will solve it using given using given information.

Q: f(x) COSX f'x) 2.

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Q: Calculate the Derivative k(u) = arc sec(u) 3u + 2

A: The given function is .The objective is to find the derivative of the given function.Derivative…

Q: Let f (x) = arcsin(x²) arctan(2x). Evaluate f'(x) =

A: Given: f′(x)=arcsin(x2)arctan(2x)Getting the derivative, we…

Q: Let ƒ(x) = − 2 sin¯¹(e8²) ƒ'(x) =

A: Given query is to find indicated derivative.

Q: If f(z) = 3 sin (z) then f'(z) =

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Q: f'(rr), where f(t) = sint cost

A: Given function is ft=sint cost To find: f'π Solution: Product rule of differentiation is:…

Q: If A and B are constants, find where f''(x) = 0 I= f(x) = 9 Ar² + 7. Bx³

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Let f(x) = 5 sec(5x) f'(x)

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Q: Solve the derivative in R3: r(t) = (cos(t), 2sin(t), et^2) x (t, t ln(t), 0)

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Q: Let f (t) = et sin 7t Part (a) Find L{f (t)} Part (b) Find L{f' (t)}

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Q: Find f. f'(t) = sec(t)(sec(t) + tan(t)), = -1 f(t) =

A: Given that: f'(t)=sect(sect+tant),    -π2<t<π2, fπ4=-1