THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{{t)} and n = 1, 2, 3, then .... L{t'{t} = (-1)" Fs). ds Evaluate the given Laplace transform. (Write your answer as a function of s.) (7 cos(t)}

Q: CoS z 5,⁰ √1+4t2 dt, find F'(x) 11. If F(x) =

A: The objective is to find F'(x).

Q: The graphs of the functions f and g are shown in the figure. y -1 Let u(x) = f(x)g(x) and v(x): =…

A: Given: Let  and To Find:

Q: Find the derivative of h(x) 3 4 sin x COS X sin x COS X 2 COS X 1+ sin x - 3 cos²x (1 + sin x)³ 2…

A: To find the derivative of .

Q: tan '(z*), , Find

A: The objective is to find ddxtan-1x4x=1 Use the formulas: ddxtan-1(x)=11+x2ddxxn=nxn-1

Q: Question 17 () Let / be defined as follows: {² z Using the definition of the derivative, compute…

A: Let f be defined as follows:  fx=x2 if x<0x if x≥0 By using the definition of derivative, to…

Q: 12:06 ■I 5G (3) Calculate the derivative f'(x) of the following function a) f(x) = √1- b) f(x) = x²…

A: Solution of the given question is like as

Q: P c=0 and I= 1. d (a) Use the definition of the derivative to prove IP d. -I" = nr"-1 for all n E…

A: Given , Function =xn To Prove :ddxxn= nxn-1  using Quotient rule

Q: (d). If (2, 3) are the coordinates of a point on the graph of y = f(x), then the point (2, –4) would…

A:

Q: Find the derivative of the function. f(0) = cos(8²) f'(0)

A: We have given We have to find the derivative of the given function.As we know from chain rule that…