Differentiate the function. y = In(12 + t – t31)

Q: Determine whether the function t(xry, 2)=x' +y-2 (where Y,/ and Ź are s tritly greater than 0) is…

A: Use Hessian matrix

Q: find extreme Value of function fex, y) = x°t 3xy?-3x²-3y=t7 1

A: Given:  fx,y=x3+3xy2-3x2-3y2+7 ⇒fx=3x2+3y2-6x, fy=6xy-6y To find extreme points put fy=0, fx=0…

Q: Approximate V128 by linearizing f(x) = VI about a = 125 . What is the result?

A: Given: 1283

Q: Find b, if the function f(t) = t?.

A: This is a Fourier analysis question. Lets solve it.

Q: Differentiate the function. R(q) = 9 ln q R(q) =

A: Given that       R(q) = 9 ln q Here we have to find R'(q).

Q: Differentiate the function with respect to the independent variable. f(s) = s³ e 4 + 8 e f'(s) =O

A:

Q: Differentiate the function with respect to the independent variable. f(s) = s° e ² + 4 e f'(s) = D

A: Given: f(s)=s6 e2+4e To determine: f'(s)

Q: c. Use antidifferentiation to find f (x).

A: Since, we have asked for solving part-(c) only.Since here it is given that f'(x)=x2 ln x -(i)Here…

Q: Determine an approximate solution of the equation z3 + 3xyz? – 5x²y²z+ 14 = 0 for z near 2, as a…

A: To determine : an approximate solution of the equation               z3+3xyz2-5x2y2z+14=0 for z near…

Q: Calculate L6 for f(x) = v6x + I over [1,3]. %3D (Give your answer to three decimal places.) L6 =

A:

Q: Differenti ate each function ) y= V+ In (+*)

A: This question is based on chain rule differentiation.

Q: Where is f(x) = differentiable? %D

A: The objective is to check where f(x) is differentiable.

Q: Find, if they exist, the extrema of the function: f(x, y) = x² + 3y? + 4,

A:

Q: Find Fxxygy for the function Fory)-J*J€nx-x]

A: We havr to find the derivative.

Q: Differentiate the following function. r(t) = (4t,8/i,

A: We have to find derivative

Q: he sand is uneven whereby the surface height, in metres, measured fr ottom of the container, is…

A: In the given question, the concept of volume is applied. Volume The volume of Cuboid is given by…

Q: Differentiate the function f(t) = yt (a + bt).

A:

Q: Differentiate the function In e* 8.) y = ex 7.) f(x) = e** – In :

A:

Q: For what value of x does the function g(x) 2x concave downward? 1/3

A: The function is concave downward when  f '' (a) < 0  at x = a

Q: find all possible functions with the givenderivative. y' = 2x

A: According to the question, we have to find all possible functions with the given derivative y'=2x.…

Q: Differentiate the following function.   y = xe

A:

Q: Plot the following functions over the interval 0<x<4 in the same a) x3 plot: b) e* c) ex2

A:

Q: Differentiate the following with respect to the variable: f(t) = 3cos2t

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (x* + 2ху — 4y?)dx — (x? — 8ху — 4у?)dy %3D 0 -

A: Explanation of the answer is as follows

Q: Differentiate the function.

A: Given function is hx=lnx+x2-1 Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: Find the second derivative of the function Y = (3x² – 5)´ A. " = 1082? + 60 B. /" = 1082? – 60 C. "…

A:

Q: Graph the function y x over the interval |-1, 1].

A: Graph

Q: Differentiate the function. F(t) = tª + e4 F'(t) =

A:

Q: Find the real and imaginary parts of the Following functions z+1 ?

A: To find real and imaginary parts of the function fz=z+1 Let  z=u+iv fz=x+iy So, the real part of fz…

Q: Differentiate the function y = Inx• In 13x. y' =O

A:

Q: Express the function in the form   f ° g  ° h

A: The given function is Rx=x-1 It is required to show the given function in the form of fogoh. So,…

Q: 2. (x? + 2ху — 4у?)dx — (x? — 8ху — 4у?)dy %3D0 -

A:

Q: Differentiate the function y=xcosx  and y=(x+1)e2x.

A:

Q: Find for the given function. w= 10z2 e?

A:

Q: State the interval(s) over which the function is (a) increasing (b) decreasing (c) constant

A:

Q: Give the interval where y is decreasing y=x²e^x

A:

Q: Differentiate the function R(q) = q° - 3 ln q. R'(q) =

A: Topic - derivative of a function

Q: Differentiate the function with respect to the independent variable. f(s) = s° e4 +3e f'(s) =D

A: Consider the given: fs=s3e4+3eDiffrentiate w.r.t.…

Q: 10. g(t) = V1+ In(t)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Sketch the level curve of the function V(x, y) x² + y? for c 64. %3D

A:

Q: Differentiate the following function. y = Vx y' =

A:

Q: End the solution and dyined the interpal at which function is depince dx

A: Given that xdydx+y=1y2Solution :xdydx+y=1y2xdydx=1y2-yxdydx=1-y3y2y21-y3dy=dxx∫y21-y3dy=∫dxxlet,…

Q: Differentiate the function. t(t? + 1)4 V2t – 1 g(t) = In 5

A: Given g(t)=lnt(t2+1)42t-15

Q: c) k(r) = e* + re %3D

A:

Q: 2. Sketch the graph of the function (a) f(x, y) = Vr² + y? (b) f(x, y) = Vx² + y? – 1 %3D

A: Given a. fx,y=x2+y2b.fx,y=x2+y2-1

Q: fand sketch it, for f(x, y) = x²

A:

Q: The amount of light intensity on a point is given by the function t2 + 2t + 16 I(t) te [0,14] t+2

A: In this question, we need to find the time of minimal intensity and the minimal intensity.

Q: he surtace f(xy) A

A: A line lies on a plane if and only if every point on the line, lies on the plane and the normal to…

Q: ind the antiderivative, G(t), of the function g(t) = (2n²t? – t*)v2n² – t2.

A: