Given f(x) = In(- 4e" – 13), f'(x) = %3D

Q: When a vertical beam of light passes through a transparent medium, the reason that its intensity I…

A: We have to find What is the beam intensity at 15 feet below the surface.

Q: Find dy/dx by implicit differentiation. xy + 5x + 2x2 = 3

A:

Q: Find the derivative of the function y = (4x + 1)4(5x + 1)-5. dy (16x+4) 3 (4x+1)4 dx (5x+1)5…

A:

Q: Find the differential dy of the given function y=extanx

A:

Q: 1. Differentiate the implicit equation with respect to x. x³ + y³ ln(x) + e²y = 4

A:

Q: Find for the following equation by Implicit Partial Differentiation; дz x³ + y²z4 + 3xyz = 5

A: Implicit partial differentiation

Q: Find the differential of the function y=√x3+4x at x=2.

A: Given the function:

Q: OFind the second derivative of y = 4Vx + E + 10

A:

Q: A company will sell N units of a product after spending $x thousand in advertising, as given by N =…

A: We are given that N=50x-x2, 5≤x≤25. Now, dN=50-2x dx. First, increase the advertising budget from…

Q: Find the partial derivative of the given In[y? sec(x²y²)].

A:

Q: Find the 4th order differential of the function y=√2x+1.

A:

Q: A population of insects grows at a rate that is given by dN = 0.078N dt - If there are initially 100…

A:

Q: 1. Compute forward approximations of O(h) and O(h² for the first derivative of y = e* evaluated at x…

A: 1st we will derive formula for O(h) and O(h2) and then find corresponding values

Q: Find the length of the curve y =x2/8 − ln(x) on the interval [1, 2].

A:

Q: The derivative of y= sech-(Inx)+e sinh- (3x) equals Select one: +3esinh (3x) cosh(3x) y' = xlnxv…

A: The derivative of y=sech-1(lnx)+esinh-1(3x) is to be calculated by chain rule. The derivative of…

Q: In (In e*1): What is the derivative of y 3z²+1

A:

Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: Consider and solve the initial value problem of a new form of life discovered on a distant planet.…

A:

Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

A:

Q: 4. FIND d²y BY IMPLICIT DIFFERENTIATION: x² + y² = 81 %3D dx2

A: Given: x2+y2=81

Q: 2. Solve x². dy + 2xy = 4x³ using an + 2xy = 4x³ using an Integrating Factor. dx

A:

Q: 15 - What is the approximate derivative of f(x) = 5x° + 4x? if we use forward difference method,…

A: Derivative of function at any point gives the slope of tangent to the function at that point.…

Q: A certain population is known to be growing at a rate given by the logistic equation = x(b – ax).…

A: Firstly find critical points. After that find second derivative , If second derivative less than…

Q: Find the nth-order differential of the function y=2x.

A: To find nth order differential of the given function.

Q: A population of wild horses is represented by the logistic differential equation dP/dt =…

A: Given: The logistic differential equation is, dpdt=0.08p-0.00004p2          (1) To find: A) The…

Q: If y = sin (4x - 5), then what is y' a. y = 4 cos (4x - 5) b. y 3 сos (4x - 5) C. y' = -cos (4x) d.…

A: In this question  we have to solve the given statements. NOTE: As per our policy we are suppose to…

Q: Find the differential of the function y=xxe2x at the point x=1.

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: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?

A: use average rate of change formula .

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: Find the differential of y² + x = 4.

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

Q: 22. Find the derivative of y = arcos(4x) with respect to x. - 4 4 - 4 - 4 В. 1-4x2 С. Vi-(4x) A. D.…

A:

Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A:

Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

Q: Can you help me step by step with this problem?

A: Differentiate both sides w.r.t. x.And for addition we can apply the derivative separately on both…

Q: 2. Approximate the derivative of f(x) forward, backward, and central difference method and step size…

A: To obtain the derivative at the point x0,y0, the following methods can be used:- The forward…

Q: If fex, yJ-o find dy /af partial derivative off dx

A:

Q: Find the linear approximation of f(x)=ln x at x=1 and use it to estimate ln(1.24). L(x)=?…

A:

Q: In x 3. Compute the approximate derivative of f(x) = · at x = 2, using three-midpoint x² + 1 formula…

A: Given is a function and at a point at which the approximate value of first derivative of the…

Q: If the first derivative of y is -3.8025 sin(0.507 t) on the interval {0 <= t <= 24}, what are the…

A:

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 ; d'y/dx 1. y = 2. Y = (7x + 2)5…

A:

Q: Find the 1st and 2nd derivatives of the following profit function: =(xa-110)1/a that is, and find…

A:

Q: Suppose x and y are functions of third variable t. In the equation *-+) , what are the values of the…

A:

Q: If y = 5x2 + 2x + 9 , find the value of the differential dy as x changes from 3 to 3.1

A: Given, y = 5x2 + 2x + 9Differentiating with respect to x;dydx = 10x + 2At x = 3, dydxx = 3 = 10×3 +…

Q: In the integration ∫dx/√9-4x^2, What is the implicit derivative of u? a. du= 2dx b. du= dx/2 c.…

A: To find: The implicit derivative of u. Given: The integration is ∫dx9-4x2. Calculation: The…

Q: What is the integrating factor of y' - 2xy x?

A:

Q: Find the first derivative 1. y = In v4-x2 %3D 2. In(x2 + y2) + 4arctan = 5 y %3D dy x+4 3. Find , if…

A: