Finding a Second Derivative In Exercises 45-50, find d?y/dx² implicitly in terms of x and y. 45. x2 + y? = 4

Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function. y = 5(2 − x3)4

A: We have to find the derivative using the chain rule of differentiation . According to the chain rule…

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Q: Ordinary Differential equation is an equation which involves * One derivative two derivative O Non…

A: an ordinary differential equation is a differential equation containing one or more functions of one…

Q: PART D. IMPLICIT FUNCTIONS, CHAIN RULE and HIGHER DERIVATIVES 14. Evaluate y" or of the function x'…

A: Given: x33+y33=132 For finding third derivative of given expression, we differentiate given…

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Q: Determine whether the differential equation is linear. Explain your reasoning.

A: Given :   To determine whether the given differential equation is linear.

Q: y = e - 2x %3D sine

A: First, find the auxiliary roots from the given equation. Use yx=c1y1+c2y2 to write complementary…

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A: Consider the given function.

Q: cx²+1 ₂. F(x) = [²² - -H (t³ - t) dx

A: We have to find derivative

Q: 2. (у — с x)dx + cos + cos x dy = 0 COS

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Q: 8. (Standard C5: Chain rule) Compute the derivative of h(x) = tan(vT). Show all of your work. You do…

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Q: Determine whether the differential equation y′ − y sin x = xy2 is linear. Explain your reasoning.

A: The given differential equation y′ − y sin x = xy2

Q: A differential equation is an equation that has at least one derivative true O false x*() +>(2)* +»*…

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Q: The order of a differential equation is the degree of the highest order derivative in the equation.…

A: Suppose a differential equation is d3ydx35+d2ydx2+dxdy6+y=0

Q: Verify that the function satisfies the differential equation. (A differential equation in x and y is…

A: Given function - y = 2sinx+3        ............(1)Differentiating with respect to x - dydx =…

Q: II. DIFFERENTIATION 1. (E- 2x) = A- 2 B.는-2 +2 D.-2 %3! 2x 2x-1 2. 21

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A: Given:

Q: Finding the first and second derivatives in detail y= A 2*

A: We will use derivative to solve the given problem .

Q: 1. y= x° – 4 x* – 2x³ + 3x² – 5x + 10 | | |

A: Explanation of the solution is given below....

Q: Finding a Derivative In Exercises 5–26, finddydx by implicit differentiation. 5. x2 + y2 = 9

A: Implicit differentiation:       Implicit differentiation is the procedure of differentiating an…

Q: Using the Alternative Form of theDerivative In Exercises 69–76, use thealternative form of the…

A: Given function is gx=x2-x. To find derivative at c=1 using alternative form of derivative. Solution:…

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A: Given,

Q: Second Derivatives Find y" in Exercises 59–64. 62. y = 9 tan (3)

A: y=9tanx3Differentiate…

Q: Derivative Calculations In Exercises 1–12, find the first and second derivatives.

A: We use the power rule to find the first derivative. Power rule: d/dx(x^n)= n*x^(n-1)

Q: , It can be helpful to classify a differential equation, so that we can predict the techniques that…

A: Note that  Linear different equation :  A differential equation is called linear if (i) every…

Q: In Exercises 33–46, find the derivative.

A: To find derivative of y=ecos-1x. Chain rule of derivative states that: ddxfgx=f'gx·g'x…

Q: Method of differentiation. 19. Solve (1-x²) dy − xdx + m²y=0 - where x = 0, y=0, x=m dx

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Q: 1 - dt -dy=C %3D

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Q: can you explain the whole process, step-by-step? like in an essay type. how did they find the first…

A: Here the question is to find the first and second derivative of the function f(x) = 12cos2x. To find…

Q: 60. Y 3r-5 cost mx) "

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Q: Write a differential equation that fits the physical description. The rate of change in the…

A: Please find attachment for the details solution

Q: Find the derivative. (The Fundamental Theorem of Calculus- Part 1) 19) у %3D cos /t dt COS

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Q: (QI] Find the general solution of the Differential Equation (DE) yo) + y = 0.

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Q: Verify that the function satisfies the differential equation. (A differential equation in x and y is…

A: Given, y=2 sinx+3 Differentiate the given equation with respect to x we get, y'=2 cosx Now again…

Q: dx 5. x + 1²x sin t %3D dt

A: Given ordinary differential equation is: xdxdt+t2x=sin t We have to solve the above equation.

Q: In Exercises 45–74, compute the derivative using derivative rules that have been introduced so far.

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Q: What is a differential form? What does it mean for such a form to be exact? How do you test for…

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Q: Verify that the function satisfies the differential equation. (A differential equation in x and y is…

A: Given differential equation, y''+y=0       ...(1)

Q: A curve has an equation x2- 6x + 2y - 8 = 0. Find the equation of tangent and normal line at x = 3…

A: Given the Equation of the curve : x2-6x+2y-8=0 ⇒2y=-x2+6x+8⇒y=12(-x2+6x+8) ⇒f(x)=12(-x2+6x+8)…

Q: In Exercises 33–46, find the derivative.

A: Consider the given function as y=cos-1t-1-sec-1t Simplify as y=cos-11t-sec-1t Use the property of…

Q: In Exercises 45–74, compute the derivative using derivative rules that have been introduced so far.

A: Consider the given function as y=cos3x+3cosx+79

Q: . Determine whether the statement is true or false. If it is true, explain why. If it false, explain…

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Q: In Exercises 13–18, calculate the derivative in two ways. First use the Product or Quotient Rule;…

A: The function h(t)=t2-1t-1. We have to calculate the derivative in two ways. First, use the Product…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: