If Fc{e¯a#} = a²+p² ' find the F's{-a e a"}

Q: With respect to x, what is the derivative of: * du In(u) O Option 2 Option 4 du Option1 Option3

A: apply chain rule

Q: Part 4: A derivative computation using the FTC and the chain rule d d (F(2*)) = dx dt |3| e dx 20

A: Topic:- application of integration and derivatives

Q: Two equivalent forms of the Chain Rule for calculating the de-rivative of y = f(g(x)) are presented…

A: Given, if y=fx and u=gx then the derivative of their composition can be expressed as

Q: Suppose that Y ~ Normal(0, 1). Compute E[Y³].

A: Solution

Q: let X~beta(a,b). find m.g.f ofY=ln| 1-x

A:

Q: 4.62. Evaluate the derivative of the Gamma function and see dT'(x) r'(x) = dx ' (In t)e"'dt

A: To differentiate the gamma function:         Γ(x) = ∫0∞tx-1e-tdt Integral definition of gamma…

Q: Find the Hessian of the function. Based on result in c), determine the types of stationary points…

A: We need to find the Hessian and stationary points of the function f(x,y)= x3+y2-2xy.

Q: 2. A college professor never finishes his lecture before the end of the hour and always finishes his…

A: Note: Since you have posted a question with two subparts, we will solve the first part for you.…

Q: Find the Tians Farm F(s) = "suy (27>1>0) (1 – s)(1 – e **) 3) f(1) = e',

A: Given problem:- Find laplace transformation of f(t) =et (0<t<2π)

Q: X₁ and X₂ are random samples from exp(). when x > 0.) (pdf of exp()=e Determine the constant c so…

A: we have given that Xi follow exponential with mean λ that is E(Xi) = λ also, X1 and X2 are…

Q: If; of t = x then at t=1 is (Note that these functions in N) dx

A:

Q: X (4) is a WSS process with E [X (t)]=2 and Ryx (T) = 4 + e- 0.1 la, Find the mean 1 and variance of…

A:

Q: Find the indicated derivative. dp for p q² + 2 5q – 3 %3D dq dp dq II

A:

Q: find the values of the derivatives ds/dt at t=0 if s = 2/(4 - t)

A: Given function is Differentiating with respect to t, we get

Q: If T, is an MVUE of y (0) and T, is any other unbiased estimator of y (0) with efficiency e < 1,…

A: Answer: For the given data,

Q: f(x, y) = 1/(xy), then the marginal pdf of X is (log x)/y. Is this statement True/False?

A:

Q: If X is an exponential RV with parameter A, find the PDF of Y = -14 In(X). 2

A: Given information: If X is an Exponential random variable with parameter λ. The pdf of X is,…

Q: If X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval…

A: Given, X is exponentially distributed with parameter λ Y is uniformly distributed on the interval…

Q: 11) If X be a r.v. from exponential distribution (x)= e- ス>0, x20 Then the moment generating…

A:

Q: Find the linearization L(x) of y = e5* In(x) at a = 1. L(x) =

A: Given that:y=e5xln(x)a=1To find the linearization

Q: Suppose X1 and X2 are iid observations from the pdf f(r|a) = ax 0. Show that (log X1)/(log X2) is an…

A:

Q: The analysis of tooth shrinkage byC. Loring Brace and colleagues at the University of Michigan’s…

A: Given: The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of…

Q: What is the derivative of the expression (xy)" = e 1+ In(xy) 1+ In(xy) y O Option 1 Option 2 1+…

A: Given (xy)x=eTo find Derivative:

Q: Use linear approximation to approximate e.03 О 1.03

A:

Q: suppose that y is an implicit function f(x) defined by the equation x^3 + y^3 = 8xy − 7. find the…

A: suppose that y is an implicit function f(x) defined by the equationx3+y3=8xy−7. find the equation of…

Q: Suppose that a population P(t) satisfies dP P F (1-500P), dt 2 where t is measured in days. Ast → ∞,…

A:

Q: If e (3x + 2)e2* dy 3 4 using logarithmic differentiation. (b) show that +2 2.x-1 %3D (2x-1) dx 3x…

A:

Q: Determine the GINI Index of Country X whose Lorenz curve is f(x) =;x² +÷x*. If Country Z 3 has a…

A: The Lorenz curve  of country X is f(x)=12x2+12x4. The GINI index  of a certain country with Lorenz…

Q: 98x2.1for one year to y

A:

Q: If X is an exponential r.v. with parameter 5, identify the r.v. 10X

A: Introduction: The random variable X has an exponential probability distribution with parameter, λ =…

Q: Suppose X - Bernoulli (0.5) and Y ~ Exponential (2). Suppose further that X and Y are independent.…

A:

Q: If Y Poisson(A) and A has pdf f(A) = e-^ for A > 0, elsewhere, find zero E(2Υ) V (2Y):

A:

Q: Find the linearization L(x) ofy = e8# ln(x) at a = 1. L(x) =

A: We will use formula for linearization at one variable.

Q: c) Solve the model for the detection of diabetes for critically damped case.

A: Given :The model for the detection of diabetes for critically damped case

Q: 1. Let X be a lifetime (in hours) of a lightbulb and suppose that X has a PDF of (e0.001x f(x) = {…

A:

Q: Compute the derivative.log(sin(t))

A: Given: ddtlog3sint To find: We have to find the given derivative.  Required formulas: logab=lnalnb…

Q: et Xi- Nco,1) and n=2 T=X,+Xz Show that Tis Sufficiencs y Statistic

A:

Q: Evaluate the derivative of e22.1.png acos(b/x) COS f(x) = x2 if a = 71 and b = 0.5 at x = 2 using…

A:

Q: Use a linear approximation (or differentials) to estimate the given number. e0.01

A: We use linear approximation to find e0.01 By linear approximation f(x)=f(a)+f'(a)(x-a) we take a=0…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.  g(x)=…

A:

Q: Apply the first order forward difference formula to find the derivative at x = 2.1. fx) 1.2 0.694444…

A: We need to find the derivative of the function f(x) at x=2.1 by applying first order forward…

Q: 3 7 use log differentiation to differentiate to find y prime (dy).   y = sin(x)x

A: Given function y = Sin(x)x , here we need to determine y\'.Let us use logarithmic differentiation.…

Q: II z= ě Y x - Juv Find dz dv üs ing chein rule.

A:

Q: find the values of the derivatives ds/dt at t=-1 if s = 1 - 3t2

A:

Q: 2. The Lorenz curve of a particular society is given by L(x) = Ax? + Bx. %3D Suppose that the…

A: We will use given values in Lorenz curve and Gini index to create equations for A and B , Then solve…

Q: Prove that by Gamma Function eit + e' e-st dt 2 s2 + 1

A: We will find out the required result using Gramma function.

Q: Which of the following graphs is the slope field for dx 12 -3-211. s 2 13 US 111-2-/35 1112 111²-111…

A: Here we have to solve the given differential equation and plot the solution

Q: et dt. · e2t 5. Find and simplify the derivative of f(x) = %3D 1 -2 In z

A: Assume g'(t) = e^t/(1-e^(2t))

Q: a) Find the marginal pdf's of X1 and X2 b) Are X1 and X2 independent? Why or why not? c) Find P(X1 <…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.