Let z= I= 2e", and y = 3 ln v. Find in terms of u and v.

Q: Evaluate 1cos ax dx and 1sin ax dx, where a is a constant.

A: We know that, ∫cosθdθ=sinθ+C           ⋯⋯1∫sinθdθ=-cosθ+C     ⋯⋯2 (a) We have, I=∫cosaxdx Let us…

Q: (a) 2-1 dx

A:

Q: B- Find dy / dx for the following functions: (3 mark) * 1- Y= sin( coshx log, 2 )

A:

Q: Find the indicated derivative or integral a. D, (3** * ) c. D, log,, (x³ +9) –3x а. D, b. |x 2* dx…

A: We know that Dx ax = ax·ln(a) Dx af(x) = af(x)·ln(a)·f'(x)   ∫ax dx = axln(a)+C   Dx loga x =…

Q: Differentiate  G(t)= Sinh(In t) G'(t)=?

A:

Q: Find the equation of tangent at x = In 5: ln 2x a) y = ²x + 1 e to :

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Write a differential formula that estimates the change in the surface area S= 6x of a cube when the…

A: Given that surface area of cube s=6x2and side length change from x0 to x0+dxsolution:x=x0  and…

Q: Use x = ey to explain why d/dx (ln x) = 1/x, for x > 0.

A:

Q: sinh x – 1 dx cosh x

A: The given integral: ∫sinh x-1cosh xdxWe need to find the antiderivatives.

Q: Find the DE by eliminating the arbitrary constant  y = A+ bex

A: Given equation  y=A+be^x Where A & b are arbitrary constant.

Q: Find dy/dx by implicit differentiation.

A: Given: x2+y2=64 To Find: dydx by implicit differentiation

Q: 1 4x2 dx X.

A:

Q: to determine the approximate value of v(1+x³)dx

A:

Q: t +t dt

A: Antiderivative: Integration is the inverse process of differentiation.  The operation of finding the…

Q: L{sinh 6t– cosh t

A: we have to find the value of L{sinh(6t)-cosh(t)}

Q: Evaluate Si S dz dæ dy 0. 4.

A: Here I am attaching image so that you understand each and every step.

Q: xe* dx Jo (1+x)

A: Given                                            I=∫01xex1+x2dx now,…

Q: This is a linear DE. If arranged to its form, what is the integrating factor? * xdy ニ

A:

Q: Without integrating, explain why: S, ?)°dx = o x(1+ x* -2

A: To show:     ∫-22x1+x22dx = 0 (without integrating)

Q: Find cosh² (t) sinh5 (t) dt.

A:

Q: L{ e¬at sinh wt} =

A:

Q: find the derivative of y with respect to x, t, or u,as appropriate.55. y = ln (cos^2 u) 56. y = ln…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: 1. dx Evaluate 0, et +e-*

A:

Q: Given tanh(x)+ tanh ¯' (y) = 1, show that, 1- y? 1 – x² dy dx

A: Formula,ddxtanh-1x=11-x2Note- Since multiple questions are asked, I am answering the first question…

Q: Find dx dy for y = Vx log, (x' – tan x). Do not simplify your ar

A:

Q: Given a function ƒ that is differentiable on its domain, write andexplain the relationship between…

A: The differentiable function is f on the interval I which contains a point a. The linear…

Q: Find dy/dx by implicit differentiation for the following.   2x + ln y = x4y4

A: Given :2x+lny = x4y4

Q: Find the most general antiderivative , verify answer by differentiation  g(x)=7sin theta/3

A:

Q: Find the total differential du. 1. w = y tan a? – 2xy

A: To find the total derivative

Q: Differentiate y= cosh vx

A: Given, y = coshx  We have to differentiate it.

Q: Jrin m In(cos m) dm

A:

Q: Take the derivative of the following: Dy= 3xe y = e (3) e y = @y= In () 10 Y=ln (In x)

A:

Q: Find de when y = In(1+ 5/æ) dx

A: The objective is to find derivative.

Q: . Let y =sqrtx Find the differential dy

A: To find, y=x To find the differential dy.

Q: 3.1.1 L sinh 3t dt

A: The Laplace transform can be obtained using the table of the transforms. The integral for the…

Q: S,Ly? e*ydydx 1-

A: Use Change of order of integration to solve given Integration.

Q: Find y′ by implicit differentiation. e^(x/y)=4x−2y y'=?

A: To calculate the value dy/dx from the provided implicit differentiation e(x/y)=4x-2y. Now,…

Q: Find the total differential. z = 10x y10 dz =

A: As we know that the: If the given function is z=fx,y then the expression for the total differential…

Q: Find dy/dx by implicit differentiation. x6+y7=45

A:

Q: obtain the ava dient to Cu gra equation givey by メ= ln and sigh '2t wh 3.

A:

Q: Find dy/dx by implicit differentiation for the following.:x + ln y = x2y3

A: The given equation is x+ln y=x2y3. Compute the derivative as follows.

Q: Find the most general antiderivative. 4 dx

A:

Q: Incot3x dx sinh e* 1+9x

A:

Q: dy Find in terms of x and y if x In y + yo = 4 ln x. dx

A: Solution is written in below steps.

Q: 60. (a) dx SI dt 1 + √t (b) de fint di dt

A: We can solve this as follows:

Q: Find the approximate value of V0.95 using differential

A:

Q: What is the derivative of r(t)=e^(4t)costi+e^(4t)sintj+e^(4t)k

A: Differentiate both sides with respect to t.

Q: Find the indicated derivative. dz if z = In (x° + e 5) dx dz dx

A: Given data is: z=lnx8+e5 To find the value of dzdx