Solve the initial value problem with y(0) = 1. y = help (formulas) dy = + 2y 40 sin(x) + 30 cos(x) dx Reminder: To find the anti-derivative of something like e" sin(u), the trick is to do integration by parts twice. Book: Section 1.4 of Notes on Diffy Qs

Q: QUESTION 3 3 1 2 Let A = 1 4 5 2 5 and X2 X= 6. X3 Find (X'AX). Write out its derivatives with…

A:

Q: Plese solve witgout AI, handwritten is prefered

A:

Q: find equation of tangent line to the graph of the given function at the indicated value of x

A:

Q: dy a. Use suitable rule of differentiation to find if dx y = sin vat and x = sin ßt.

A: Applying parametric conditions of derivative

Q: please utilise implicit differentiation to calculate dy/dx if you are given:  a) (x^2)+(y^2)+xy=3…

A:

Q: Find the derivative of g(x) = e * x). sin (1+ 0-3x²e*cos(1+x°) O xe*1sin(1+x°)+3x²e*cos(1+x) O…

A: The product rule of derivatives states that duv=u'v+v'u.

Q: 7. In a certain country, the number of people (in millions) using their mobile phones to check…

A: Given query is to find the derivative of the function at different points.

Q: 33-34 For what values of x does the graph of f have a horizontal tangent? Hercnt 33. f(x) = x + 2…

A: we have f(x) = x+2sin x

Q: can you help with this practice problem

A: Step 1: Step 2: Step 3: Step 4:

Q: en+1=Xn+1-r=Xn- = en By Taylor's Theorem, we have f(xn) f'(xn) Putting this in Equation (2) leads to…

A: In this problem we are to check if the Newton's formula was changed to Xn+1= Xn- f(Xn)/f'(X0)We will…

Q: Find dy/dx by implicit differentiation. 5x + y = 8 + x²y²

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Solve Sin (3x) %3D cos (2x)

A: to find derivative of y=sin3xcos2x

Q: 1. Kgothatso showed her classmates that dx%3D (x- 1) Without showing Kgothatso how you would…

A: 1.AgreeGiven Integral can be evaluated with the formula :∫yndy =yn+1n+1here y =x-1 , n=-23

Q: dy 5. Find the derivative, dx' x²y = x3 – exy

A:

Q: Given the function f (x) = xe 4*, find the equation of the tangent line at the point (-1, -e*).

A:

Q: Question 13. Given that f(æ) = e2" sin 3æ, find f'(x) as a function of æ. f'(x) =

A:

Q: Use implicit differentiation to evaluate az/ax at (1, −2, 1) if x³z − 3xy² – (yz)³ = -1 -

A:

Q: Find dx dx || by implicit differentiation. 6x² + 7xy - y² = 8

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

Q: Question 4 Given the following equation, determine y'using the methods discussed in class a - y3 =…

A:

Q: Part 1 Find the equation of the tangent line to the curve a(x) = 3 sin x+In(x2 - 5x +1) – e-6z at a…

A:

Q: (ii) Hence, by using Leibniz Rule for Differentiation Under the Integral Sign, compute the value of…

A: Leibniz Rule for Differentiation under integral sign:- ∂∂t∫atbtfx, tdx=∫atbt∂f∂tdx   + fbt, t∂bt∂t-…

Q: 47. x¹ + x3 = 0, (1, 2)

A:

Q: Find 2. by Implicit Differentiation method dx k+5 = 8

A: Use implicit differentiation method find dy/dx.If

Q: 1. Use the fact that coshx = (e* + e) and sinhx = 1 NIH (ex - e-*) to solve for 1 coshx+ sinhx dx

A: ∫exdx=ex+c