Laplace Transformation f(t) = t^3 sint f(t) = ( 1 + cosht) ^ 2 f(t) = sin ^ 2 ( t + π ) f(t) = sin5tcos2t

Q: Find the derivative

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the derivative. 26) dx 16t7 dt A) B) 2x5 - 2 C) 16x7/2 D) 8x3 sin t 1 27) du 25 - u2 1 - Cos t…

A: 26) To find the derivative  ddx∫1x16t7dt First find the integral ∫1x16t7dt=16∫1xt7dt…

Q: use LaPlace transforms find solutions for dx/dt+3x=e^-2t, given that t=0 and x=2.

A: The objective of this question is to solve the given differential equation dx/dt + 3x = e^-2t using…

Q: Consider the function f(x)=2cos(x) is it a sinusoidal function? Show all work. Explain why

A:

Q: f'u where f(u) =ln(cos(g(2u)))

A: We have to find the derivative of given composition function

Q: lim t →0  (e^6t i + (sin(7t)/ (7t)) j + e^−4t k)

A: Limit :

Q: derivative 2 of the Fundamental Theorem of Calculus. √²₁ (61²-1) 22 dt 6+2 dt (61²-1) 22 dit

A: Given query is to find the derivative.

Q: Now H= [² 2 id 2² H эрг = Ho 2² [Ho Sin (Kr_wt)] ar 2 [2 Ho Sin (Kr- wt) Ho 2/ [cos (kr-wt) x] K Ho…

A: They have derived the partial derivative. Our aim is to explain the derivative rule.

Q: (6) Find the derivative where it exists (c) Where is flz) analytic ?

A:

Q: hCt)-5t (1-ビ ((チ1) (け)

A: Given query is to find the derivative of the expression using product rule.