Given that F(x) = Vt? + 1 dt calculate F"(x).

Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: Find the total differential dw. 1 5. w = x tan¬' y – 2ªyz -

A: Solved below

Q: x² S cos(VE) dt dx 'x

A: Given ddx∫xx2costdt

Q: Another particle has a velocity function of v(t) = [' 2'-* dx. What is the acceleration of this…

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Q: Solve for an autonomous equation? dy/dt = f(y)

A: An autonomous first-order ordinary differential equation is an equation of the form

Q: Find F '(x). sin(x) F(x) = 3Vt dt

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Q: Find dx/dt given that 4x^2+9y^2=13x  x=1,  y=-1 and dy/dt = 10

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Q: Find dy at taal dt and ya Vltx? and X = t.

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

Q: If sin(x) f(x)= 68+t2 dt Jtan(x) and g(y)= f(x) dx , Then g) is equal to

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Q: suppose y = √(3x + 1), where x and y are both functions of t. If dx/dt = 2, find dy/dt when x=5

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Q: Find the value of dy/ dt at t = 0 if y = 3 sin 2x and x = t2 +π.

A: Given : y=3sin2x, x=t2+π To find : dydt We can write dydt as, dydt=dydx×dxdt                    1…

Q: Find the derivative d dy dy (3y?) = ay + by +c- dt dt dt

A: Proceed as shown below....

Q: Suppose that x=x(t) and y=y(t) are both functions of t. If x2 + y2 =17, and dx/dt=2 when x=4 and…

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Q: 3. Water is being poured into a 10 liter leaky container so that the volume of the water, V,…

A: A differential equation is an equation that contains functions and their derivatives.  A…

Q: find the values of the derivatives ds/dt at t=0 if s = 2/(4 - t)

A: Given function is Differentiating with respect to t, we get

Q: Find the derivative of y with respect to t. y=e(cos t+ln t) dy/dt=???

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Q: Find the derivative of the function. s=t° In t| ds dt

A: The solution is given below in the next step:

Q: Use Part 2 of the Fundamental Theorem of Calculus to find th. derivatives. dt sin y dy 1+ y? (b) dx…

A: Consider the integral ∫axfydy, where a is a constant. Note that, ∫axfydy will be a function in x.…

Q: given xy+x2y=2 such that dx/dt=2 in/sec. Find dy/dt for x=1

A: Consider the equation and

Q: if xy+x=12 and dx/dt=-3, then what is dy/dt when x=2 and y=5?

A: Given :xy +x = 12

Q: dz If z = e2x+ 3y and x = In t, y = t2, calculate from the total dt derivative formula and show that…

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Q: A particle moves along the x-axis with velocity dx/dt = ƒ(x). Show that the particle’s acceleration…

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Q: y = tan (5t - 21 +1)

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Q: If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: Given,

Q: dz Find dt if z = x²y – sin y, x = vt? +1 and y = e -

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Q: If L = 2x2 + y2, dx/dt = -1, and dy/dt = 3, find dL/dt when x = 5 and y = 1

A: Consider the provided equation and information,

Q: + iwe¬lwt = 0. dt = 0,

A: Given differential equation is

Q: A particle moves in a straight line and any time t seconds, its velocity v m/s is given dx by e-".…

A: Note that velocity is rate of change of displacement. Hence displacement will be integration of…

Q: Let xy = 1 and dy/dt = 3. Find dx/dt when x = 1?

A: Consider a function u(x) such that, Now, according to chain rule,  The given information is,

Q: 1. xy + z2

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Q: Find the total differential. z = 5x3y8 dz =

A: The solution is:

Q: Find dy/dt using the given values. dy dt y = x² - 6x for x = 1, dx/dt = 3.

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Q: The heat transfer rate of the rocket engine is given by: dT Q = -kA dx

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Q: Compute the derivative: d I/ In(t° + 1) dt dx

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Q: Find the total differential. z = 6x1°y8 dz =

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Q: "Differentiate both sides of the equation V = Tr*with respect to t AP (using the chain rule on the…

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Q: In integrating the function fx In 5x dx using integration by parts, what would be your v?

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Q: Use the method of first principles to show that d/dt(lnt)=1/t

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Q: Find the total differential dw. 5. w = x tan¬ y – 2ªyz

A: The objective is to find total derivative dw.

Q: Find the indicated derivative. dy dt - for y = (2.2t - 4t?)(2t + 1.9) dt 11

A: We have to find dy/dt for Given function.

Q: Find dy/dt using the given values. y = x3 - 5x for x = 3, dx/dt = 4. dy dt

A: Value of dy/dt= 88 See the calculation below

Q: Assume that 2x + 3y = 12 and dy/dt = -2. Find dx/dt.

A: Assume,

Q: Find the total differential. z = 10x6y7 dz =

A: Differentiation of xⁿ = nxn-1

Q: Find the total differential. z = 10x y10 dz =

A: As we know that the: If the given function is z=fx,y then the expression for the total differential…

Q: Calculate cln 2 I = Ver – 1 dx thanks to the change of variable u Ver – 1. U = -

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Q: If y = x2 and dx/dt = 3, then what is dy/dt when x = -1?

A: Differentiate both sides with respect to t.

Q: Q10.a) Find rsinx if tnx Jt +5 dt + siny = x – x²cosy

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Q: Find the total differential. z = 6x *y5 iz

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Q: If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y. TRUE or FALSE ?

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Q: dy dt II

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.