Eliminate the arbitrary constants of  y=e^(-3x) (Acos5x - Bsin5x) + Cx Where A, B,  and C are the arbitrary constants

Q: Find the solution of the equation y= 2x -x- 10 in the interval (2, 4] using derivatives. You can use…

A: To solve an equation  f(x)=0 using derivative of function, we can use the formula…

Q: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

Q: the equation ariables x and y and

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Q: If 4x2 + 2x + ry = 1 and y(1) = - 5, find y'(1) by implicit differentiation.

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Q: Explain the derivatives and integration.

A: Solution: Derivatives: Definition of derivatives is , the rate of change of a quantity with respect…

Q: Find the slope and equation of tangent line y=4-x^3, (-1,5)

A: Consider the given equation: y=4-x3 The point where tangent has to be calculated is (-1,5)

Q: Find y" by implicit differentiation. 3x3 + 4y3 = 2

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Q: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

Q: 6. у3 2x – Jx² – 1

A: Given function y=12x-x2-1 we want to derivative of given function with respect to x

Q: x³tanh² (x*) sech²(x*) dx

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Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" :

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Q: Calculate the derivative.

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 5 - -2, and the line 4…

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Q: бх + 5 -, is 10х + 8 The derivative of y =

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Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" =

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Q: The number of licensed drivers in a country (in millions) can be approximated by the function g(x) =…

A: Here, the given function is: g(x)=178.277x0.065 where x is the number of years and g(x) is the…

Q: Suppose you are climbing a hill whose shape is given by the equationz= 1000−0.01x2−0.02y2, where x,…

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Q: Find the derivatives of the functions in Exercis

A: Given, y=5-2x-3+182x+14

Q: Find the derivative. y = ecosh(8x) y'(x) =

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Q: If 5a + 3x + ry = 1 and y(1) = - 7, find y'(1) by implicit differentiation.

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Q: Find the equation of a that has a y" = 4 if it has a slope of of 3 Curve Second derivative %3D at…

A: equation of the curve  is given below...

Q: A population of 200 rodents is growing at a rate of 5% per month. What equation model can represent…

A: The exponential growth or decay is modelled using the equation, f(t)=a(1±r)t, where a is the initial…

Q: Find the equation of a curve going through the point (3, 7) and having slope 4x² – 3 at (x, y).

A: Given ,Slope of curve is 4x2-3Thereforedydx=4x2-3Taking integationon both…

Q: Differentiate the function. y = etan(8) y' =

A: The given function is y=etanθ.

Q: The population of Glenbrook is 375,000and is increasing at the rate of 2.25% per year. Predict when…

A: To find: When the population is 1 million. Given: Initial population is 375000 and rate of…

Q: one leg of a right triangle is 1 in/min and the other leg increases 2 inches per min. What is the…

A: Let the first leg of the right triangle be a and the other leg be b. Let the hypotenuse of the right…

Q: If 2x^2+3x+xy=5 and y(5)=-12, find y’(5) by implicit differentiation

A: Given:- 2x2+3x+xy=5 , y(5) =-12 To find:- y'(5) by implicit differentiation

Q: 2dx 4х-3

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

Q: Find y" by implicit differentiation. 4x3 + 5y3 = 6 У" :

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Q: Suppose the amount of oil pumped from one of canyon near the beach of island decreases at the…

A: Given query is to find the time when output will become one fifth of initial value.

Q: Find the slope of the tangent lines on the curve y = 6x^3 +24x^2 -39x -43 at poins (-5, 2) and (1/3,…

A: We know that, The slope of the tangent line to the curve at a given point Px1,y1 is equal to the…

Q: If 3x + 3x + xy 4 and y(4) = - 14, find y' (4) by implicit differentiation.

A: According to question,Given equation,3x2 + 3x + xy = 4,y4 = -14

Q: A colony of bacteria with originally 100 cells has now grown to 900 in 2 hours. Assuming the rate of…

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Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 30x + 0.8x2 −…

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Q: If 5x^2+2x+xy=4 and y(4)= -21, find y’(4) by implicit differentiation.

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Q: Find y" by implicit differentiation. 5x3 + 4y3 = 9 У" - %3D

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Q: Find the second derivative of y = -5 %3D -

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Q: Explain how to find a first partial derivative of a function oftwo variables.

A: To get the first partial derivative of a function z = f(x, y) with respect to x we have to…

Q: Find if x- costy =- cscy

A: Given that: x-cos2y=xcscy

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x – 2x and…

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Q: ength of the curve 1 1 < x < 2. 6 10x3 +

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Q: Find y" by implicit differentiation. 4x3 + 5y3 = 1 y" =

A: We will find the y" of the given function using the implicit differentiation.Below find the solution…

Q: Find the first derivative by increment method. Show your complete solution. V12x – 3 Irolim Exam…

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Q: Find 1" and 2nd order partial derivative for the function ax²+by²+2hxy and also verify дхду дудх

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Q: A rectangle’s length is growing at 3 inches per second, while its width is shrinking at 5 inches per…

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Q: Find the area bounded by the curve 4 square units 8 square units 16 square units 10 square units =…

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Q: Calculate the second and the third derivative of y = 5x- 9 y": y"

A: Using derivatives rule &amp; formula.