3. Let f(x) = In (5x² + 2x). %3D Graph both f (x) and f'(x) with your graphing technology. Find f'(1), f'(2) , ƒ'(3) , ƒ'(-1) , f'(-2).

Q: dy/dx if y=tan((1-2x)/(1+x)) dy/dx if y=x^4 ln(3x-1)

A: 1)    y=tan1-2x1+x2)    y=x4ln(3x-1) Hint:  Chain rule and then uv and u/v rule of differentiation

Q: Compute the indicated derivative using the chain rule. dy x = 4 + 3t, y = -7t; dx dy dx ||

A:

Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = Sin2x ; 0<x<n

A: i) The given function is fx=sin2x. Given that the domain of the function is 0,π. Obtain the first…

Q: Q2 find the derivative of the following: 1) y = 2stn²(5x) ,2) y = Inx'n cosh 5x ,3) xsin¬14y = y…

A:

Q: Question 1 Find the total differential of the function z = 7x³y8 Odz = 7x¹y³dx + 7x³y+dy dz =…

A:

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

A:

Q: 5. Find of the parameters: x = sin 2t and y = - cost at t = dx %3D

A: Topic = Derivative

Q: Compute dy/dx for the function. y = sinh 2 8x O 2 sinh 8x cosh 8x O 2 cosh 8x 16 sinh 8x cosh 8x 16…

A:

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

A: Implicit partial differentiation

Q: Find the partial derivative. 17zy

A: Given, ∂xe17xy∂x We have to find the partial derivative.

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

A:

Q: Find dx at x--3 if y-5x-2 and Do NOT Round.

A:

Q: Given a right circular cone with an altitude of 5 cm and a base diameter of 8 cm. If the diameter is…

A: volume of cone =Πr2h/3

Q: What is the derivative 7 of y = (3x + 1)²? 21 dx dy = 6 (3x + 1)²¹ dx = dy 6 (3x + 1)² dx = 7 (3x +…

A:

Q: find x which minimizes the following function and its minimum with differentiation technique.…

A: We will find out the required solution.

Q: Find the derivative of y with respect to x. y = tan 1 (In 4x) 1+ (In 4x)2 xV1+ (In 4x)² x(1 + (In…

A: We will find the derivative of y with respect to x as following.

Q: |х — 1 x5

A: Use the method of substitution to evaluate the integral. I=∫x−1x5dx=∫x−1x52dxLet u=xdu=12xdxSo,…

Q: 2 1 Estimate -dx using the right endpoint rule with n = 4 3 1+x

A:

Q: Differentiate. y =x° In x- dy II

A:

Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

A:

Q: If we are getting the partial derivative of f(x,y) with respect to x, we are letting the y variable…

A: hello greetings from bartelby.i am here to help you.

Q: Determine the indicated (in the attached image) partial derivative of z = x4y5 - cos(x3y2)

A:

Q: Find dy/dx by implicit differentiation. 6,,3 x°y - y = x dy/dx

A: On implicit differentiation we differentiate both sides of the equation with respect to x . Then we…

Q: 11. Find the length of the curve x = on the interval (2, 4] (integrate with respect to y) 12y3 un

A: Given that the function x =y55+112y3 Find the arc length of the graph of the given curve on the…

Q: 23, zax + sec(x)cos(y) 0, y(0) = 0

A:

Q: Please show me the partial derivatives for this homogenous equation and solve for GS/PS using Test…

A: Exact differential equation

Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8

Q: Find a result by using homogenous for (x³ - 3x²y)dx-(x3³ - y³)dy = 0

A: This question is based on solution of Homogeneous differential equation.

Q: Find the partial derivative. 4 = (x² + 6x – 3y)* - dz

A:

Q: Find dy/dx by implicit differentiation. 5x3 + x2y − xy3 = 2

A:

Q: find dy/dx of y=sin^2 4x+1/2 cos 8x

A: Given,         y=sin24x+12cos8x

Q: Determine the indicated (in the attached image) partial derivative of  f(x, y) = 3x3y2 + ln(2x2 -…

A:

Q: 1 By considering the secant through the points where x = 1.2 and x = instantaneous rate of change of…

A:

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: What is (V | and find the relative minimum dx point as indicated by the black dot on the graph at…

A: Here we have ;  y=xx ..................(1) taking log both of sides

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

A:

Q: Find the indicated partial derivative: dy \ y + 4x ду

A:

Q: The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor…

A: A. Profit Function : P(X) = R(x) - C(x) P(x) = -0.04x2 + 800x - 130x + 40000 P(x) = -0.04x2 + 670x +…

Q: Find the derivative. 8) y = (x + 1)2(x2 + 1)-3 dy dx dy = -2(x + 1)(x2 + 1)-4(2x2 + 3x – 1) A) B) Y…

A: We can find the correct answer as below.

Q: Evaluate the integrals

A: Given integral is:

Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two numbers:= 750; Sum of one and 10times the other is minimum;

Q: Find dy/dx at (-4,1) if xy=(8y/(x+2)). dy/dx at (-4,1) =?

A: Derivative of any function determines the rate of change of a function. It is represented as dydx if…

Q: Find explict solution of the foilowing initial-value problem dy yoanx?, yla)of %3D dx

A:

Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.

Q: Approximate the derivative of y=x² at x=1 by forming small changes

A: We have to find the derivative of the function y=x2 at x = 1 by forming the small changes.

Q: 5. Find by implicit differentiation for x + y = xy. dx

A: